diff --git a/experiments/Synth/.gitignore b/experiments/Synth/.gitignore
index e20e245..f9dfacf 100644
--- a/experiments/Synth/.gitignore
+++ b/experiments/Synth/.gitignore
@@ -413,3 +413,5 @@ $RECYCLE.BIN/
 
 ## Acknowledgements
 # Many thanks to `https://gitignore.io/`, written and maintained by Joe Blau, which contributed much material to this gitignore file.
+
+.direnv
diff --git a/experiments/Synth/Manifest.toml b/experiments/Synth/Manifest.toml
index 36b3449..62cdbaa 100644
--- a/experiments/Synth/Manifest.toml
+++ b/experiments/Synth/Manifest.toml
@@ -2,12 +2,12 @@
 
 julia_version = "1.10.2"
 manifest_format = "2.0"
-project_hash = "db74a993eef408d9b910e97f9a72ec5fee351591"
+project_hash = "2ce1bc403a7f2a6b21dfce6ff771dac87eae8621"
 
 [[deps.ADTypes]]
-git-tree-sha1 = "e1ce448a0d7f88168ffe2eeac4549c32d45a42d1"
+git-tree-sha1 = "fb97701c117c8162e84dfcf80215caa904aef44f"
 uuid = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
-version = "1.12.1"
+version = "1.13.0"
 weakdeps = ["ChainRulesCore", "ConstructionBase", "EnzymeCore"]
 
     [deps.ADTypes.extensions]
@@ -64,12 +64,13 @@ version = "0.1.41"
 
 [[deps.Adapt]]
 deps = ["LinearAlgebra", "Requires"]
-git-tree-sha1 = "50c3c56a52972d78e8be9fd135bfb91c9574c140"
+git-tree-sha1 = "cd8b948862abee8f3d3e9b73a102a9ca924debb0"
 uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
-version = "4.1.1"
-weakdeps = ["StaticArrays"]
+version = "4.2.0"
+weakdeps = ["SparseArrays", "StaticArrays"]
 
     [deps.Adapt.extensions]
+    AdaptSparseArraysExt = "SparseArrays"
     AdaptStaticArraysExt = "StaticArrays"
 
 [[deps.AliasTables]]
@@ -287,6 +288,12 @@ git-tree-sha1 = "664021fefeab755dccb11667cc96263ee6d7fdf6"
 uuid = "caabdcdb-0ab6-47cf-9f62-08858e44f38f"
 version = "1.1.1"
 
+[[deps.Clingo_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "daeebbde7f084416d3ec585b5d23a1590b3a87ce"
+uuid = "e1d4ad0e-dc8b-5d2d-8155-e9a55b531f08"
+version = "5.7.1+0"
+
 [[deps.CloseOpenIntervals]]
 deps = ["Static", "StaticArrayInterface"]
 git-tree-sha1 = "05ba0d07cd4fd8b7a39541e31a7b0254704ea581"
@@ -307,15 +314,15 @@ version = "1.3.6"
 
 [[deps.CodecZlib]]
 deps = ["TranscodingStreams", "Zlib_jll"]
-git-tree-sha1 = "545a177179195e442472a1c4dc86982aa7a1bef0"
+git-tree-sha1 = "962834c22b66e32aa10f7611c08c8ca4e20749a9"
 uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
-version = "0.7.7"
+version = "0.7.8"
 
 [[deps.ColorSchemes]]
 deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"]
-git-tree-sha1 = "26ec26c98ae1453c692efded2b17e15125a5bea1"
+git-tree-sha1 = "403f2d8e209681fcbd9468a8514efff3ea08452e"
 uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
-version = "3.28.0"
+version = "3.29.0"
 
 [[deps.ColorTypes]]
 deps = ["FixedPointNumbers", "Random"]
@@ -397,15 +404,15 @@ version = "0.2.3"
 
 [[deps.ConcurrentUtilities]]
 deps = ["Serialization", "Sockets"]
-git-tree-sha1 = "f36e5e8fdffcb5646ea5da81495a5a7566005127"
+git-tree-sha1 = "d9d26935a0bcffc87d2613ce14c527c99fc543fd"
 uuid = "f0e56b4a-5159-44fe-b623-3e5288b988bb"
-version = "2.4.3"
+version = "2.5.0"
 
 [[deps.CondaPkg]]
-deps = ["JSON3", "Markdown", "MicroMamba", "Pidfile", "Pkg", "Preferences", "TOML"]
-git-tree-sha1 = "905244d4b8d2319783a39df4e7c7eb9e9bb022d8"
+deps = ["JSON3", "Markdown", "MicroMamba", "Pidfile", "Pkg", "Preferences", "Scratch", "TOML", "pixi_jll"]
+git-tree-sha1 = "bebaee53d574063ba9a563823248b766e9841255"
 uuid = "992eb4ea-22a4-4c89-a5bb-47a3300528ab"
-version = "0.2.24"
+version = "0.2.25"
 
 [[deps.Configurations]]
 deps = ["ExproniconLite", "OrderedCollections", "TOML"]
@@ -501,16 +508,18 @@ uuid = "85a47980-9c8c-11e8-2b9f-f7ca1fa99fb4"
 version = "0.4.4"
 
 [[deps.DiffEqBase]]
-deps = ["ArrayInterface", "ConcreteStructs", "DataStructures", "DocStringExtensions", "EnumX", "EnzymeCore", "FastBroadcast", "FastClosures", "FastPower", "ForwardDiff", "FunctionWrappers", "FunctionWrappersWrappers", "LinearAlgebra", "Logging", "Markdown", "MuladdMacro", "Parameters", "PreallocationTools", "PrecompileTools", "Printf", "RecursiveArrayTools", "Reexport", "SciMLBase", "SciMLOperators", "SciMLStructures", "Setfield", "Static", "StaticArraysCore", "Statistics", "TruncatedStacktraces"]
-git-tree-sha1 = "b1e23a7fe7371934d9d538114a7e7166c1d09e05"
+deps = ["ArrayInterface", "ConcreteStructs", "DataStructures", "DocStringExtensions", "EnumX", "EnzymeCore", "FastBroadcast", "FastClosures", "FastPower", "FunctionWrappers", "FunctionWrappersWrappers", "LinearAlgebra", "Logging", "Markdown", "MuladdMacro", "Parameters", "PrecompileTools", "Printf", "RecursiveArrayTools", "Reexport", "SciMLBase", "SciMLOperators", "SciMLStructures", "Setfield", "Static", "StaticArraysCore", "Statistics", "TruncatedStacktraces"]
+git-tree-sha1 = "df4954f297a09f05e1f84a049566ae93d5304477"
 uuid = "2b5f629d-d688-5b77-993f-72d75c75574e"
-version = "6.161.0"
+version = "6.164.1"
 
     [deps.DiffEqBase.extensions]
     DiffEqBaseCUDAExt = "CUDA"
     DiffEqBaseChainRulesCoreExt = "ChainRulesCore"
     DiffEqBaseDistributionsExt = "Distributions"
     DiffEqBaseEnzymeExt = ["ChainRulesCore", "Enzyme"]
+    DiffEqBaseForwardDiffExt = ["ForwardDiff"]
+    DiffEqBaseGTPSAExt = "GTPSA"
     DiffEqBaseGeneralizedGeneratedExt = "GeneralizedGenerated"
     DiffEqBaseMPIExt = "MPI"
     DiffEqBaseMeasurementsExt = "Measurements"
@@ -525,6 +534,8 @@ version = "6.161.0"
     ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
     Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
     Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
+    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+    GTPSA = "b27dd330-f138-47c5-815b-40db9dd9b6e8"
     GeneralizedGenerated = "6b9d7cbe-bcb9-11e9-073f-15a7a543e2eb"
     MPI = "da04e1cc-30fd-572f-bb4f-1f8673147195"
     Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7"
@@ -666,12 +677,6 @@ git-tree-sha1 = "71d0768dd78ad62d3582091bf338d98af8bbda67"
 uuid = "21656369-7473-754a-2065-74616d696c43"
 version = "1.1.1"
 
-[[deps.Expronicon]]
-deps = ["MLStyle", "Pkg", "TOML"]
-git-tree-sha1 = "fc3951d4d398b5515f91d7fe5d45fc31dccb3c9b"
-uuid = "6b7a57c9-7cc1-4fdf-b7f5-e857abae3636"
-version = "0.8.5"
-
 [[deps.ExproniconLite]]
 git-tree-sha1 = "c13f0b150373771b0fdc1713c97860f8df12e6c2"
 uuid = "55351af7-c7e9-48d6-89ff-24e801d99491"
@@ -750,9 +755,9 @@ weakdeps = ["HTTP"]
 
 [[deps.FilePathsBase]]
 deps = ["Compat", "Dates"]
-git-tree-sha1 = "7878ff7172a8e6beedd1dea14bd27c3c6340d361"
+git-tree-sha1 = "2ec417fc319faa2d768621085cc1feebbdee686b"
 uuid = "48062228-2e41-5def-b9a4-89aafe57970f"
-version = "0.9.22"
+version = "0.9.23"
 weakdeps = ["Mmap", "Test"]
 
     [deps.FilePathsBase.extensions]
@@ -878,15 +883,15 @@ version = "0.2.0"
 
 [[deps.GR]]
 deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Preferences", "Printf", "Qt6Wayland_jll", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "p7zip_jll"]
-git-tree-sha1 = "9bf00ba4c45867c86251a7fd4cb646dcbeb41bf0"
+git-tree-sha1 = "0ff136326605f8e06e9bcf085a356ab312eef18a"
 uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
-version = "0.73.12"
+version = "0.73.13"
 
 [[deps.GR_jll]]
 deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "FreeType2_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Qt6Base_jll", "Zlib_jll", "libpng_jll"]
-git-tree-sha1 = "36d5430819123553bf31dfdceb3653ca7d9e62d7"
+git-tree-sha1 = "9cb62849057df859575fc1dda1e91b82f8609709"
 uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
-version = "0.73.12+0"
+version = "0.73.13+0"
 
 [[deps.GeoFormatTypes]]
 git-tree-sha1 = "8e233d5167e63d708d41f87597433f59a0f213fe"
@@ -901,9 +906,9 @@ version = "1.4.1"
 
 [[deps.GeometryBasics]]
 deps = ["EarCut_jll", "Extents", "GeoInterface", "IterTools", "LinearAlgebra", "PrecompileTools", "Random", "StaticArrays"]
-git-tree-sha1 = "f0895e73ba6c469ec8efaa13712eb5ee1a3647a3"
+git-tree-sha1 = "3ba0e2818cc2ff79a5989d4dca4bc63120a98bd9"
 uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
-version = "0.5.2"
+version = "0.5.5"
 
 [[deps.GeometryTypes]]
 deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "StaticArrays"]
@@ -936,7 +941,7 @@ uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
 version = "2.82.4+0"
 
 [[deps.GraphDynamicalSystems]]
-deps = ["AbstractTrees", "DocStringExtensions", "DynamicalSystems", "FileIO", "Graphs", "HerbConstraints", "HerbCore", "HerbGrammar", "HerbSearch", "MLStyle", "MetaGraphsNext", "Random", "SoleLogics", "Statistics"]
+deps = ["AbstractTrees", "DocStringExtensions", "DynamicalSystemsBase", "FileIO", "Graphs", "HerbConstraints", "HerbCore", "HerbGrammar", "HerbSearch", "MLStyle", "MetaGraphsNext", "Random", "SciMLBase", "SoleLogics", "StaticArrays", "Statistics"]
 path = "../.."
 uuid = "13529e2e-ed53-56b1-bd6f-420b01fca819"
 version = "0.2.0"
@@ -976,11 +981,17 @@ git-tree-sha1 = "55c53be97790242c29031e5cd45e8ac296dadda3"
 uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
 version = "8.5.0+0"
 
+[[deps.Herb]]
+deps = ["HerbConstraints", "HerbCore", "HerbGrammar", "HerbInterpret", "HerbSearch", "HerbSpecification", "Reexport"]
+git-tree-sha1 = "9674e956ee337397790bb9293382f5ff91acc804"
+uuid = "c09c6b7f-4f63-49de-90d9-97a3563c0f4a"
+version = "0.5.0"
+
 [[deps.HerbConstraints]]
 deps = ["DataStructures", "HerbCore", "HerbGrammar", "MLStyle"]
-git-tree-sha1 = "3367f188d76fcf1c9fee626dc2a9110674f480a5"
+git-tree-sha1 = "4864ee127e354c33c0e8fc5b87a179d52bc0967c"
 uuid = "1fa96474-3206-4513-b4fa-23913f296dfc"
-version = "0.2.5"
+version = "0.3.0"
 
 [[deps.HerbCore]]
 deps = ["AbstractTrees"]
@@ -1002,9 +1013,9 @@ version = "0.1.6"
 
 [[deps.HerbSearch]]
 deps = ["DataStructures", "HerbConstraints", "HerbCore", "HerbGrammar", "HerbInterpret", "HerbSpecification", "MLStyle", "Random", "StatsBase"]
-git-tree-sha1 = "95a5c1e87cd61b14cf9785f293e5633b39a69fc5"
+git-tree-sha1 = "76f72e8045ae4ea862e1f698a831f18f2cb0f7fb"
 uuid = "3008d8e8-f9aa-438a-92ed-26e9c7b4829f"
-version = "0.4.1"
+version = "0.4.3"
 
 [[deps.HerbSpecification]]
 deps = ["AutoHashEquals"]
@@ -1070,9 +1081,9 @@ uuid = "d25df0c9-e2be-5dd7-82c8-3ad0b3e990b9"
 version = "0.1.5"
 
 [[deps.InlineStrings]]
-git-tree-sha1 = "45521d31238e87ee9f9732561bfee12d4eebd52d"
+git-tree-sha1 = "6a9fde685a7ac1eb3495f8e812c5a7c3711c2d5e"
 uuid = "842dd82b-1e85-43dc-bf29-5d0ee9dffc48"
-version = "1.4.2"
+version = "1.4.3"
 
     [deps.InlineStrings.extensions]
     ArrowTypesExt = "ArrowTypes"
@@ -1104,9 +1115,9 @@ weakdeps = ["Unitful"]
 
 [[deps.IntervalArithmetic]]
 deps = ["CRlibm_jll", "LinearAlgebra", "MacroTools", "RoundingEmulator"]
-git-tree-sha1 = "eb6ca9aef11db0c08b7ac0a5952c6c6ba6fbebf0"
+git-tree-sha1 = "0fcf2079f918f68c6412cab5f2679822cbd7357f"
 uuid = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
-version = "0.22.22"
+version = "0.22.23"
 
     [deps.IntervalArithmetic.extensions]
     IntervalArithmeticDiffRulesExt = "DiffRules"
@@ -1198,6 +1209,12 @@ version = "1.14.1"
     [deps.JSON3.weakdeps]
     ArrowTypes = "31f734f8-188a-4ce0-8406-c8a06bd891cd"
 
+[[deps.Jieko]]
+deps = ["ExproniconLite"]
+git-tree-sha1 = "2f05ed29618da60c06a87e9c033982d4f71d0b6c"
+uuid = "ae98c720-c025-4a4a-838c-29b094483192"
+version = "0.2.1"
+
 [[deps.JpegTurbo_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "eac1206917768cb54957c65a615460d87b455fc1"
@@ -1206,9 +1223,9 @@ version = "3.1.1+0"
 
 [[deps.JuliaInterpreter]]
 deps = ["CodeTracking", "InteractiveUtils", "Random", "UUIDs"]
-git-tree-sha1 = "a729439c18f7112cbbd9fcdc1771ecc7f071df6a"
+git-tree-sha1 = "4bf4b400a8234cff0f177da4a160a90296159ce9"
 uuid = "aa1ae85d-cabe-5617-a682-6adf51b2e16a"
-version = "0.9.39"
+version = "0.9.41"
 
 [[deps.Kaleido_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
@@ -1253,9 +1270,9 @@ version = "1.4.0"
 
 [[deps.Latexify]]
 deps = ["Format", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Requires"]
-git-tree-sha1 = "ce5f5621cac23a86011836badfedf664a612cee4"
+git-tree-sha1 = "cd714447457c660382fe634710fb56eb255ee42e"
 uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
-version = "0.16.5"
+version = "0.16.6"
 
     [deps.Latexify.extensions]
     DataFramesExt = "DataFrames"
@@ -1511,6 +1528,12 @@ version = "1.2.0"
 [[deps.Mmap]]
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 
+[[deps.Moshi]]
+deps = ["ExproniconLite", "Jieko"]
+git-tree-sha1 = "453de0fc2be3d11b9b93ca4d0fddd91196dcf1ed"
+uuid = "2e0e35c7-a2e4-4343-998d-7ef72827ed2d"
+version = "0.3.5"
+
 [[deps.MozillaCACerts_jll]]
 uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
 version = "2023.1.10"
@@ -1625,9 +1648,9 @@ version = "1.4.3"
 
 [[deps.OpenSSL_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
-git-tree-sha1 = "7493f61f55a6cce7325f197443aa80d32554ba10"
+git-tree-sha1 = "a9697f1d06cc3eb3fb3ad49cc67f2cfabaac31ea"
 uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
-version = "3.0.15+3"
+version = "3.0.16+0"
 
 [[deps.OpenSpecFun_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl"]
@@ -1660,9 +1683,9 @@ version = "1.8.0"
 
 [[deps.OrdinaryDiffEqCore]]
 deps = ["ADTypes", "Accessors", "Adapt", "ArrayInterface", "DataStructures", "DiffEqBase", "DocStringExtensions", "EnumX", "FastBroadcast", "FastClosures", "FastPower", "FillArrays", "FunctionWrappersWrappers", "InteractiveUtils", "LinearAlgebra", "Logging", "MacroTools", "MuladdMacro", "Polyester", "PrecompileTools", "Preferences", "RecursiveArrayTools", "Reexport", "SciMLBase", "SciMLOperators", "SciMLStructures", "SimpleUnPack", "Static", "StaticArrayInterface", "StaticArraysCore", "SymbolicIndexingInterface", "TruncatedStacktraces"]
-git-tree-sha1 = "6a58da59c5f7640fd09636231bd73dfb4744ce53"
+git-tree-sha1 = "2f31fd2e015223f7e196f6d0e8a2a9c34b6a1bdc"
 uuid = "bbf590c4-e513-4bbe-9b18-05decba2e5d8"
-version = "1.15.1"
+version = "1.18.1"
 weakdeps = ["EnzymeCore"]
 
     [deps.OrdinaryDiffEqCore.extensions]
@@ -1687,9 +1710,9 @@ version = "0.11.32"
 
 [[deps.Pango_jll]]
 deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "FriBidi_jll", "Glib_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl"]
-git-tree-sha1 = "ed6834e95bd326c52d5675b4181386dfbe885afb"
+git-tree-sha1 = "3b31172c032a1def20c98dae3f2cdc9d10e3b561"
 uuid = "36c8627f-9965-5494-a995-c6b170f724f3"
-version = "1.55.5+0"
+version = "1.56.1+0"
 
 [[deps.Parameters]]
 deps = ["OrderedCollections", "UnPack"]
@@ -1744,10 +1767,22 @@ uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
 version = "1.4.3"
 
 [[deps.PlotlyBase]]
-deps = ["ColorSchemes", "Dates", "DelimitedFiles", "DocStringExtensions", "JSON", "LaTeXStrings", "Logging", "Parameters", "Pkg", "REPL", "Requires", "Statistics", "UUIDs"]
-git-tree-sha1 = "56baf69781fc5e61607c3e46227ab17f7040ffa2"
+deps = ["ColorSchemes", "Colors", "Dates", "DelimitedFiles", "DocStringExtensions", "JSON", "LaTeXStrings", "Logging", "Parameters", "Pkg", "REPL", "Requires", "Statistics", "UUIDs"]
+git-tree-sha1 = "90af5c9238c1b3b25421f1fdfffd1e8fca7a7133"
 uuid = "a03496cd-edff-5a9b-9e67-9cda94a718b5"
-version = "0.8.19"
+version = "0.8.20"
+
+    [deps.PlotlyBase.extensions]
+    DataFramesExt = "DataFrames"
+    DistributionsExt = "Distributions"
+    IJuliaExt = "IJulia"
+    JSON3Ext = "JSON3"
+
+    [deps.PlotlyBase.weakdeps]
+    DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
+    Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+    IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a"
+    JSON3 = "0f8b85d8-7281-11e9-16c2-39a750bddbf1"
 
 [[deps.PlotlyJS]]
 deps = ["Base64", "Blink", "DelimitedFiles", "JSExpr", "JSON", "Kaleido_jll", "Markdown", "Pkg", "PlotlyBase", "PlotlyKaleido", "REPL", "Reexport", "Requires", "WebIO"]
@@ -1843,9 +1878,9 @@ version = "0.2.2"
 
 [[deps.Polynomials]]
 deps = ["LinearAlgebra", "OrderedCollections", "RecipesBase", "Requires", "Setfield", "SparseArrays"]
-git-tree-sha1 = "56ff43adee1b1449fa151265b0088fe1c14dfd7d"
+git-tree-sha1 = "0973615c3239b1b0d173b77befdada6deb5aa9d8"
 uuid = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
-version = "4.0.14"
+version = "4.0.17"
 
     [deps.Polynomials.extensions]
     PolynomialsChainRulesCoreExt = "ChainRulesCore"
@@ -1871,18 +1906,6 @@ git-tree-sha1 = "17275485f373e6673f7e7f97051f703ed5b15b20"
 uuid = "85a6dd25-e78a-55b7-8502-1745935b8125"
 version = "0.2.4"
 
-[[deps.PreallocationTools]]
-deps = ["Adapt", "ArrayInterface", "ForwardDiff"]
-git-tree-sha1 = "6c62ce45f268f3f958821a1e5192cf91c75ae89c"
-uuid = "d236fae5-4411-538c-8e31-a6e3d9e00b46"
-version = "0.4.24"
-
-    [deps.PreallocationTools.extensions]
-    PreallocationToolsReverseDiffExt = "ReverseDiff"
-
-    [deps.PreallocationTools.weakdeps]
-    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
-
 [[deps.PrecompileSignatures]]
 git-tree-sha1 = "18ef344185f25ee9d51d80e179f8dad33dc48eb1"
 uuid = "91cefc8d-f054-46dc-8f8c-26e11d7c5411"
@@ -1981,9 +2004,9 @@ version = "6.7.1+1"
 
 [[deps.QuadGK]]
 deps = ["DataStructures", "LinearAlgebra"]
-git-tree-sha1 = "cda3b045cf9ef07a08ad46731f5a3165e56cf3da"
+git-tree-sha1 = "9da16da70037ba9d701192e27befedefb91ec284"
 uuid = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
-version = "2.11.1"
+version = "2.11.2"
 
     [deps.QuadGK.extensions]
     QuadGKEnzymeExt = "Enzyme"
@@ -2029,9 +2052,9 @@ version = "2.1.1"
 
 [[deps.RecursiveArrayTools]]
 deps = ["Adapt", "ArrayInterface", "DocStringExtensions", "GPUArraysCore", "IteratorInterfaceExtensions", "LinearAlgebra", "RecipesBase", "StaticArraysCore", "Statistics", "SymbolicIndexingInterface", "Tables"]
-git-tree-sha1 = "ea6ad53c168c7c1c2e8f870aefda269692a8a91f"
+git-tree-sha1 = "a967273b0c96f9e55ccb93322ada38f43e685c49"
 uuid = "731186ca-8d62-57ce-b412-fbd966d074cd"
-version = "3.28.0"
+version = "3.30.0"
 
     [deps.RecursiveArrayTools.extensions]
     RecursiveArrayToolsFastBroadcastExt = "FastBroadcast"
@@ -2102,9 +2125,9 @@ version = "0.5.1+0"
 
 [[deps.Roots]]
 deps = ["Accessors", "CommonSolve", "Printf"]
-git-tree-sha1 = "f233e0a3de30a6eed170b8e1be0440f732fdf456"
+git-tree-sha1 = "e52cf0872526c7a0b3e1af9c58a69b90e19b022e"
 uuid = "f2b01f46-fcfa-551c-844a-d8ac1e96c665"
-version = "2.2.4"
+version = "2.2.5"
 
     [deps.Roots.extensions]
     RootsChainRulesCoreExt = "ChainRulesCore"
@@ -2131,18 +2154,6 @@ git-tree-sha1 = "04c968137612c4a5629fa531334bb81ad5680f00"
 uuid = "7e49a35a-f44a-4d26-94aa-eba1b4ca6b47"
 version = "0.5.13"
 
-[[deps.SBML]]
-deps = ["DocStringExtensions", "IfElse", "Libdl", "SBML_jll", "SparseArrays", "Unitful"]
-git-tree-sha1 = "95a41304024735a61f2d5425265c6e7e75967766"
-uuid = "e5567a89-2604-4b09-9718-f5f78e97c3bb"
-version = "1.6.0"
-
-[[deps.SBML_jll]]
-deps = ["Artifacts", "JLLWrappers", "Libdl", "XML2_jll", "Zlib_jll"]
-git-tree-sha1 = "7567084bd3defc697c168b8b0ab3d28a9bc47648"
-uuid = "bb12108a-f4ef-5f88-8ef3-0b33ff7017f1"
-version = "5.20.1+0"
-
 [[deps.SHA]]
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
 version = "0.7.0"
@@ -2153,13 +2164,14 @@ uuid = "94e857df-77ce-4151-89e5-788b33177be4"
 version = "0.1.0"
 
 [[deps.SciMLBase]]
-deps = ["ADTypes", "Accessors", "ArrayInterface", "CommonSolve", "ConstructionBase", "Distributed", "DocStringExtensions", "EnumX", "Expronicon", "FunctionWrappersWrappers", "IteratorInterfaceExtensions", "LinearAlgebra", "Logging", "Markdown", "PrecompileTools", "Preferences", "Printf", "RecipesBase", "RecursiveArrayTools", "Reexport", "RuntimeGeneratedFunctions", "SciMLOperators", "SciMLStructures", "StaticArraysCore", "Statistics", "SymbolicIndexingInterface"]
-git-tree-sha1 = "46c4a97031b9437d5adbb382958820a8ee188c64"
+deps = ["ADTypes", "Accessors", "ArrayInterface", "CommonSolve", "ConstructionBase", "Distributed", "DocStringExtensions", "EnumX", "FunctionWrappersWrappers", "IteratorInterfaceExtensions", "LinearAlgebra", "Logging", "Markdown", "Moshi", "PrecompileTools", "Preferences", "Printf", "RecipesBase", "RecursiveArrayTools", "Reexport", "RuntimeGeneratedFunctions", "SciMLOperators", "SciMLStructures", "StaticArraysCore", "Statistics", "SymbolicIndexingInterface"]
+git-tree-sha1 = "2242fd564bb0202a22a91f575dc58b8820612b6b"
 uuid = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
-version = "2.72.2"
+version = "2.75.0"
 
     [deps.SciMLBase.extensions]
     SciMLBaseChainRulesCoreExt = "ChainRulesCore"
+    SciMLBaseMLStyleExt = "MLStyle"
     SciMLBaseMakieExt = "Makie"
     SciMLBasePartialFunctionsExt = "PartialFunctions"
     SciMLBasePyCallExt = "PyCall"
@@ -2170,6 +2182,7 @@ version = "2.72.2"
     [deps.SciMLBase.weakdeps]
     ChainRules = "082447d4-558c-5d27-93f4-14fc19e9eca2"
     ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+    MLStyle = "d8e11817-5142-5d16-987a-aa16d5891078"
     Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
     PartialFunctions = "570af359-4316-4cb7-8c74-252c00c2016b"
     PyCall = "438e738f-606a-5dbb-bf0a-cddfbfd45ab0"
@@ -2248,9 +2261,9 @@ version = "1.1.0"
 
 [[deps.SlurmClusterManager]]
 deps = ["Distributed"]
-git-tree-sha1 = "19eb15c1c07ec60a57aef3e860c3363e5aec8f4c"
+git-tree-sha1 = "82273a8cf6beab2043a0fcfe00884bc68fafc817"
 uuid = "c82cd089-7bf7-41d7-976b-6b5d413cbe0a"
-version = "0.1.5"
+version = "1.0.0"
 
 [[deps.Sockets]]
 uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
@@ -2324,9 +2337,9 @@ weakdeps = ["OffsetArrays", "StaticArrays"]
 
 [[deps.StaticArrays]]
 deps = ["LinearAlgebra", "PrecompileTools", "Random", "StaticArraysCore"]
-git-tree-sha1 = "02c8bd479d26dbeff8a7eb1d77edfc10dacabc01"
+git-tree-sha1 = "e3be13f448a43610f978d29b7adf78c76022467a"
 uuid = "90137ffa-7385-5640-81b9-e52037218182"
-version = "1.9.11"
+version = "1.9.12"
 weakdeps = ["ChainRulesCore", "Statistics"]
 
     [deps.StaticArrays.extensions]
@@ -2380,9 +2393,9 @@ version = "0.5.7"
 
 [[deps.StringManipulation]]
 deps = ["PrecompileTools"]
-git-tree-sha1 = "a6b1675a536c5ad1a60e5a5153e1fee12eb146e3"
+git-tree-sha1 = "725421ae8e530ec29bcbdddbe91ff8053421d023"
 uuid = "892a3eda-7b42-436c-8928-eab12a02cf0e"
-version = "0.4.0"
+version = "0.4.1"
 
 [[deps.StructTypes]]
 deps = ["Dates", "UUIDs"]
@@ -2401,9 +2414,9 @@ version = "7.2.1+1"
 
 [[deps.SymbolicIndexingInterface]]
 deps = ["Accessors", "ArrayInterface", "RuntimeGeneratedFunctions", "StaticArraysCore"]
-git-tree-sha1 = "fd2d4f0499f6bb4a0d9f5030f5c7d61eed385e03"
+git-tree-sha1 = "d6c04e26aa1c8f7d144e1a8c47f1c73d3013e289"
 uuid = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
-version = "0.3.37"
+version = "0.3.38"
 
 [[deps.TOML]]
 deps = ["Dates"]
@@ -2632,9 +2645,9 @@ version = "0.3.4"
 
 [[deps.XML2_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Zlib_jll"]
-git-tree-sha1 = "a2fccc6559132927d4c5dc183e3e01048c6dcbd6"
+git-tree-sha1 = "b8b243e47228b4a3877f1dd6aee0c5d56db7fcf4"
 uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
-version = "2.13.5+0"
+version = "2.13.6+1"
 
 [[deps.XSLT_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "XML2_jll", "Zlib_jll"]
@@ -2799,9 +2812,9 @@ version = "1.2.13+1"
 
 [[deps.Zstd_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
-git-tree-sha1 = "622cf78670d067c738667aaa96c553430b65e269"
+git-tree-sha1 = "446b23e73536f84e8037f5dce465e92275f6a308"
 uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
-version = "1.5.7+0"
+version = "1.5.7+1"
 
 [[deps.eudev_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "gperf_jll"]
@@ -2893,15 +2906,21 @@ version = "1.52.0+1"
 
 [[deps.oneTBB_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
-git-tree-sha1 = "7d0ea0f4895ef2f5cb83645fa689e52cb55cf493"
+git-tree-sha1 = "d5a767a3bb77135a99e433afe0eb14cd7f6914c3"
 uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
-version = "2021.12.0+0"
+version = "2022.0.0+0"
 
 [[deps.p7zip_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
 version = "17.4.0+2"
 
+[[deps.pixi_jll]]
+deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl"]
+git-tree-sha1 = "f349584316617063160a947a82638f7611a8ef0f"
+uuid = "4d7b5844-a134-5dcd-ac86-c8f19cd51bed"
+version = "0.41.3+0"
+
 [[deps.x264_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
diff --git a/experiments/Synth/Project.toml b/experiments/Synth/Project.toml
index 3317191..384d500 100644
--- a/experiments/Synth/Project.toml
+++ b/experiments/Synth/Project.toml
@@ -2,8 +2,10 @@ name = "Synth"
 
 [deps]
 AbstractTrees = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
+Attractors = "f3fd9213-ca85-4dba-9dfd-7fc91308fec7"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
+Clingo_jll = "e1d4ad0e-dc8b-5d2d-8155-e9a55b531f08"
 CondaPkg = "992eb4ea-22a4-4c89-a5bb-47a3300528ab"
 DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
 Distributed = "8ba89e20-285c-5b6f-9357-94700520ee1b"
@@ -14,6 +16,7 @@ Git = "d7ba0133-e1db-5d97-8f8c-041e4b3a1eb2"
 GraphDynamicalSystems = "13529e2e-ed53-56b1-bd6f-420b01fca819"
 GraphRecipes = "bd48cda9-67a9-57be-86fa-5b3c104eda73"
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
+Herb = "c09c6b7f-4f63-49de-90d9-97a3563c0f4a"
 HerbConstraints = "1fa96474-3206-4513-b4fa-23913f296dfc"
 HerbCore = "2b23ba43-8213-43cb-b5ea-38c12b45bd45"
 HerbGrammar = "4ef9e186-2fe5-4b24-8de7-9f7291f24af7"
@@ -34,7 +37,6 @@ ProgressBars = "49802e3a-d2f1-5c88-81d8-b72133a6f568"
 ProgressMeter = "92933f4c-e287-5a05-a399-4b506db050ca"
 PythonCall = "6099a3de-0909-46bc-b1f4-468b9a2dfc0d"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
-SBML = "e5567a89-2604-4b09-9718-f5f78e97c3bb"
 SlurmClusterManager = "c82cd089-7bf7-41d7-976b-6b5d413cbe0a"
 SoleLogics = "b002da8f-3cb3-4d91-bbe3-2953433912b5"
 StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"
diff --git a/experiments/Synth/notebooks/make_asp.jl b/experiments/Synth/notebooks/make_asp.jl
new file mode 100644
index 0000000..9407527
--- /dev/null
+++ b/experiments/Synth/notebooks/make_asp.jl
@@ -0,0 +1,705 @@
+### A Pluto.jl notebook ###
+# v0.20.8
+
+using Markdown
+using InteractiveUtils
+
+# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
+macro bind(def, element)
+    #! format: off
+    return quote
+        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
+        local el = $(esc(element))
+        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
+        el
+    end
+    #! format: on
+end
+
+# ╔═╡ b402713a-02a9-11f0-1bca-69b96cd9c786
+using DrWatson
+
+# ╔═╡ ca420cdc-208a-4341-8409-b2e826dcf9d7
+begin
+	quickactivate(pwd())
+	using Synth
+	using ProgressMeter, DataFrames, HerbSearch, GraphDynamicalSystems, Random
+	using MetaGraphsNext: labels
+	using Statistics: quantile
+	using DynamicalSystems
+	using Clingo_jll
+	using Plots
+	using Graphs
+	using GraphRecipes
+end
+
+# ╔═╡ 73a912bb-3f03-4190-a4b8-7d3352b541ff
+using BenchmarkTools
+
+# ╔═╡ df97a629-608b-45d0-815d-0a6c1d37d95c
+using PlutoUI
+
+# ╔═╡ f09edd39-ffeb-4850-b29e-b38565273ff5
+md"""
+## Creating an ASP Model for the Local Solution Assignment Problem
+
+As input to the problem, we need to define the following ingredients:
+
+- `entity(...).`
+- `state(...).`
+- `solution(...).`
+- `steady(...).`
+
+as well as mappings between ingredients:
+
+- `belongs_to(solution, entity).`
+- `connects(solution, state, state).`
+
+### Entity Definitions
+
+The `entity` definition is easy. Just a list of the entities.
+"""
+
+# ╔═╡ 701cca9d-f8de-4160-8f5d-c1ce30d31525
+md"""
+### State Definitions
+
+For the local synthesis problems, we select a set of trajectories to synthesize from. The result of the local synthesis problem gives us information about which candidate solution connects which pairs of adjacent states.
+"""
+
+# ╔═╡ 690734ed-bdbf-4635-a4d2-37500fcea3cf
+md"""
+### Solution Definitions
+
+Currently, we are storing the candidate solutions (expressions) and their scores in a 4-tuple:
+
+> `(expression, score, per-transition-success, id)`
+
+We extract the ID, and create a unique ID for the solution by prepending the candidate name.
+"""
+
+# ╔═╡ 51f9d1b9-304e-417f-9925-b572a90e278e
+md"""
+!!! warning
+	I'm currently pruning too much, so this is not working. Solving for an assignment is still fast (<1s) so for now this doesn't matter.
+"""
+
+# ╔═╡ f298831c-8954-4957-a2b9-92f7b0cf9ca7
+md"""
+### Steady States
+
+To mark which states are steady, we need to load the original Boolean Network model and extract them.
+"""
+
+# ╔═╡ b8265bb9-83d4-4bfd-9480-a9b55d78495e
+begin
+	model_df = collect_results(datadir("src_parsed", "biodivine_benchmark_as_metagraphs"););
+	path2id = path -> parse(Int, splitext(basename(path))[1])
+	model_df.ID = path2id.(model_df.path)
+end
+
+# ╔═╡ 437a480c-e63d-40f2-9d01-dd95275a333c
+@assert model_df.ID[1] == 7 # assuming we only have the results for model 7 loaded
+
+# ╔═╡ 7e86270e-0faf-4b05-b5b2-f446d62e3320
+original_model = model_df.metagraph_model[1]
+
+# ╔═╡ 003f7d18-1801-4eda-9092-1d8685e41da6
+original_aeon = """
+\$v_Coup_fti: !(v_Fgf8 | v_Sp8) | !(v_Sp8 | v_Fgf8)
+\$v_Emx2: v_Coup_fti & !(v_Fgf8 | v_Sp8 | v_Pax6)
+\$v_Fgf8: v_Fgf8 & v_Sp8 & !v_Emx2
+\$v_Pax6: v_Sp8 & !(v_Emx2 | v_Coup_fti)
+\$v_Sp8: v_Fgf8 & !v_Emx2
+""" |> (x -> replace(x, "v_" => "", "\$" => "", "!" => "¬", "|" => "∨", "&" => "∧", "\n" => "\n"))
+
+# ╔═╡ cf9bb61c-7892-4b0b-91fe-e9c437be849d
+Markdown.parse("""
+```clingo
+$original_aeon
+```
+""")
+
+# ╔═╡ e699ff65-d7cc-4a9b-80b8-1fe4b17bb6ea
+plot(
+	reverse(original_model.graph);
+	names=Dict([k => v.value[3:end] for (k, v) in original_model.vertex_labels]),
+	nodecolor=:lightblue
+)
+
+# ╔═╡ 38bcaaaf-5ddb-4536-b270-4b93caba66c2
+(_, target_basins) = get_basins_bn(original_model)
+
+# ╔═╡ 17aa2324-3b02-47c9-8c91-9bbdd4c3cb4a
+steady_states = Iterators.flatten(values(target_basins)) |> collect
+
+# ╔═╡ 7d8c46e2-c03a-4e50-ab5a-336b58b28115
+for s in steady_states
+	for x in s
+		print("[$x], ")
+	end
+	println()
+end
+
+# ╔═╡ 749b6a19-a723-4df4-a37f-4d2d30f8d4e7
+md"""
+---
+
+### Belongs-To Definitions
+
+This might seem useless for now, because the entity is also in the solution name, but it is necessary with the way the model is currently defined. Otherwise, Clingo would not know the mapping.
+"""
+
+# ╔═╡ 50f0fcd3-e181-4d71-b833-8b67886806ab
+md"""
+### Connects Definitions
+
+From our 4-tuple of results, we now need the `per-transition-success`, which looks like a vector of `BitVectors` (maybe should be a `BitArray`?).
+
+> ```
+> BitVector[[1, 0], [0, 1], [0, 1], [1, 0], [1, 0]]
+> ```
+
+The above `BitVectors` correspond to a solution that connects the first IO example from left (input) to right (output), the second from right to left, and so on.
+
+So, to create the `connects(solution, state, state)` needs a map from the pairs to
+"""
+
+# ╔═╡ 7a58b03d-41d0-4380-85d2-231646807c5e
+md"""
+## Model Construction
+
+Now that we have all of the ingredients, we can build the model and send it to Clingo to solve.
+
+### Extra Checks
+
+First, some checks to make sure the definitions above are correct-ish.
+
+1. Are the entities lowercase, and only consisting of letters and numbers? Do they start with a letter?
+"""
+
+# ╔═╡ 458d40a7-b695-4307-aaae-b84ec75b1f56
+md"""
+2. Is there at least one state?
+"""
+
+# ╔═╡ 73360b3d-d702-4d82-9923-6aa7dccc08cf
+md"""
+3. Do all of the solution names start with one of the entity names from `vertex_names`? Are they followed by digits? Are they split with an underscore?
+"""
+
+# ╔═╡ 0dce9e1f-ad34-4a6a-b467-9517ee980f63
+md"""
+4. Does the pruning result in the same number of solutions as the "fingerprints" of solutions from their `per-transition-success` information?
+"""
+
+# ╔═╡ 32009cc3-b6de-4797-bc32-6bec42964d30
+md"""
+5. Does the pruning result in the same number of solutions `per-transition-success` information **per entity**?
+"""
+
+# ╔═╡ f5f4843c-eb6d-47e1-91c2-f92a817ce1e4
+md"""
+### Build Model File
+"""
+
+# ╔═╡ 1141d91e-ee98-4740-9765-ce1aa4f178cf
+model_def = """
+
+% For every entity, assign one solution. That solution must belong to the entity.
+1 { assign(SOLUTION, ENTITY) : belongs_to(SOLUTION, ENTITY) } 1 :- entity(ENTITY).
+
+% Edges connect states X and Y if a solution connects them and that solution is assigned
+edge(X, Y) :- connects(SOLUTION, X, Y), assign(SOLUTION, _).
+% A self-edge exists if X is steady and is a state
+edge(X, X) :- steady(X), state(X).
+% A path exists between X and Z if a an edge directly connects them
+path(X, Z) :- edge(X, Z).
+% A path from X to Z also exists if an edge connects X to an intermediate Y
+% for which there exists a path connecting Y to Z
+path(X, Z) :- edge(X, Y), path(Y, Z).
+
+% :- state(X), steady(Y), not path(X, Y).
+% There is a conflict if there is a non-steady state X and a steady state Y
+% where there is not a path between X and Y
+% conflict(X, Y)
+:- state(X), not steady(X), steady(Y), not path(X, Y), path(Y, X).
+% all states should have one outgoing edge
+% conflict(X)
+:- state(X), not path(X, _).
+:- state(Y), steady(Y), state(X), not steady(X), path(Y, X).
+
+% Output
+% #show entity /1.
+#show assign /2.
+%#show edge /2.
+%#show conflict /1.
+"""
+
+# ╔═╡ 5207cff2-6f14-4ced-a7c3-bcb5e899b83a
+md"""
+## Run Model
+"""
+
+# ╔═╡ 3010c862-fb99-4993-9109-d90b1ab04e46
+md"""
+Filter? $(@bind filtered PlutoUI.CheckBox(default=true))
+"""
+
+# ╔═╡ 02155e62-04d9-4c66-b29a-e4bb53e467d2
+md"""
+### Examine Solution
+
+One solution from the unfiltered model is
+
+> `assign(sp8_3210,sp8) assign(emx2_1128,emx2) assign(coupfti_3218,coupfti) assign(pax6_9228,pax6) assign(fgf8_5146,fgf8)`
+"""
+
+# ╔═╡ 26153e85-5a49-4376-a9ad-0e55ad6d1329
+assignments = [
+	"sp8_3210",
+	"emx2_1128",
+	"coupfti_3218",
+	"pax6_9228",
+	"fgf8_5146"
+]
+
+# ╔═╡ a434481a-e609-4a6d-a9cb-f0136672afff
+
+
+# ╔═╡ 1de6aafa-9012-4027-a754-7e3ca811fb6a
+md"""
+All of the assignments should be in the solution names list.
+"""
+
+# ╔═╡ 1337307b-163c-4eb2-8d1f-702637837d01
+md"""
+What is their index in the original solutions? We need this to examine their transitions.
+"""
+
+# ╔═╡ b06e9728-6482-4082-baf5-d3ad63f02b16
+first_transition = [
+	BitVector([true, true]),
+	BitVector([true, true]),
+	BitVector([true, true]),
+	BitVector([true, true]),
+	BitVector([true, true]),
+]
+
+# ╔═╡ a5e7fab3-8e13-4e88-a452-72ac0617055a
+md"""
+### Examine Solution Edges
+"""
+
+# ╔═╡ ba1a2fcd-f825-4d06-aecf-486ea3584c5b
+res_filtered = "edge(20,20) edge(10,10) assign(sp8_1409,sp8) assign(emx2_1393,emx2) assign(coupfti_1,coupfti) assign(pax6_6325,pax6) assign(fgf8_20,fgf8) edge(1,2) edge(4,3) edge(6,5) edge(8,7) edge(10,9) edge(11,12) edge(10,13) edge(3,14) edge(15,8) edge(6,11) edge(10,16) edge(2,14) edge(13,17) edge(4,18) edge(15,13) edge(12,1) edge(19,9) edge(20,2) edge(21,15) edge(16,18) conflict(1,20) conflict(2,20) conflict(3,20) conflict(4,20) conflict(5,20) conflict(6,20) conflict(7,20) conflict(8,20) conflict(9,20) conflict(11,20) conflict(12,20) conflict(13,20) conflict(14,20) conflict(15,20) conflict(16,20) conflict(17,20) conflict(18,20) conflict(19,20) conflict(21,20) conflict(1,10) conflict(2,10) conflict(3,10) conflict(4,10) conflict(5,10) conflict(6,10) conflict(7,10) conflict(8,10) conflict(9,10) conflict(11,10) conflict(12,10) conflict(13,10) conflict(14,10) conflict(15,10) conflict(16,10) conflict(17,10) conflict(18,10) conflict(19,10) conflict(21,10)"
+
+# ╔═╡ 6feceb12-f887-4fed-a9a1-c085267188b5
+res_sat = "edge(20,20) edge(10,10) assign(sp8_2282,sp8) assign(emx2_6156,emx2) assign(coupfti_3214,coupfti) assign(pax6_4797,pax6) assign(fgf8_1104,fgf8) edge(1,2) edge(7,8) edge(9,10) edge(3,4) edge(5,6) edge(11,12) edge(3,14) edge(13,10) edge(6,11) edge(4,18) edge(8,15) edge(14,2) edge(16,10) edge(17,13) edge(15,13) edge(12,1) edge(2,20) edge(19,9) edge(18,16) edge(21,15) edge(15,21) edge(16,18)"
+
+# ╔═╡ 2457d4f1-a93f-407d-9e53-4e44f721568b
+edges = res_sat |> split |> filter(startswith("edge")) .|> (x -> x[5:end]) .|> x -> replace(x, r"[()]" => "") .|> (x -> split(x, ",")) .|> (((x, y),) -> Pair(parse(Int, x), parse(Int, y)))
+
+# ╔═╡ d50e737f-4bb2-40a7-a906-663a2d296cc1
+graph = SimpleDiGraphFromIterator(Edge.(edges))
+
+# ╔═╡ 113a60e4-8ef5-4d37-a978-d4ac9299d649
+plot(graph; markersize=0.25, fontsize=6, names=1:length(graph), curves=true, 
+	method=:spring,
+	# nodesize=1,
+	self_edge_size=0.2
+)
+
+# ╔═╡ 4d863e2c-e9a5-4c32-8776-5427744ff411
+graph.fadjlist
+
+# ╔═╡ 3eff6e0d-79d2-4974-afaf-cfffbc620bf4
+md"""
+### Setup
+"""
+
+# ╔═╡ 8d6fe0bd-b670-47a6-91c6-0f1db32584ad
+PlutoUI.TableOfContents()
+
+# ╔═╡ c3c26128-0e7e-4475-a057-591f74aec047
+df = collect_results(datadir("exp_raw", "biodivine_search"));
+
+# ╔═╡ c081cd85-b5af-4208-9ca8-90e2b1c02d0f
+vertex_names_str = df.vertex_names |> unique |> only .|> x -> x[3:end]
+
+# ╔═╡ 4f017c2b-7f3d-4ff8-95ba-6581c55ee5f3
+vertex_names = replace.(lowercase.(vertex_names_str), "_" => "")
+
+# ╔═╡ ed8ac9f3-e361-4e05-a160-bbb5e3c2b2a1
+entity_string = "entity($(join(vertex_names, ";")))."
+
+# ╔═╡ 0fe52af5-b1d2-4b7b-aab1-8bb34044a8e5
+entity_string
+
+# ╔═╡ 3bff2b94-eef4-4185-be8f-1bca5774ff13
+@assert all(vertex_names |> Iterators.flatten |> collect |> filter(isletter) .|> islowercase)
+
+# ╔═╡ 61442d48-1005-4caa-af78-138dfcecc064
+@assert all(vertex_names |> Iterators.flatten |> collect |> filter(!isletter) .|> isdigit)
+
+# ╔═╡ a1a95edc-2a28-48a1-84cf-6b1ed635ae34
+@assert all(vertex_names .|> (x -> isletter(x[1])))
+
+# ╔═╡ e1421a5b-11c7-44a8-b6f0-4654489a2b81
+states = df.selected_trajectories |> Iterators.flatten |> Iterators.flatten |> unique
+
+# ╔═╡ 8a2c00df-b9a9-42a2-ac0c-e243527545af
+ids = eachindex(states)
+
+# ╔═╡ 1c9ab992-a1d4-4a03-af70-358389149f15
+state_string = "state(1..$(ids.stop))."
+
+# ╔═╡ 5f6aa260-a6d7-4605-9a58-585b403f52e0
+state_string
+
+# ╔═╡ 79c72d39-c2af-4b5e-8370-49f8e652a733
+@assert all(x -> x in states, steady_states)
+
+# ╔═╡ fdd9a8d5-7bc0-4121-94d9-f6259e44e240
+steady_ids = findfirst.(.==(steady_states), (states,))
+
+# ╔═╡ 17cad63a-2003-4500-acef-a02c5567a428
+steady_state_string = "steady($(join(steady_ids, ";")))."
+
+# ╔═╡ dc058b46-0fa2-4197-a151-11ef46c892a7
+steady_state_string
+
+# ╔═╡ 4de0dced-294b-46c8-bb8a-c36922bf9df1
+function raw_connection_builder(solution_name, successes, specifications)
+	@assert length(successes) == length(specifications)
+	raw_connections = Tuple{Int, Int}[]
+	for (success, spec) in zip(successes, specifications)
+		id1 = findfirst(==(spec[1]), states)
+		id2 = findfirst(==(spec[2]), states)
+		if success[1]
+			push!(raw_connections, (id1, id2))
+		end
+
+		if success[2]
+			push!(raw_connections, (id2, id1))
+		end
+	end
+
+	return raw_connections
+end
+
+# ╔═╡ 15ac2c7c-c01c-4c3c-a145-84bbdfb788ca
+function connection_builder(solution_name, successes, specifications)
+	@assert length(successes) == length(specifications)
+	connection_strings = String[]
+	connects = (x, a, b) -> "connects($x, $a, $b)."
+	for (success, spec) in zip(successes, specifications)
+		id1 = findfirst(==(spec[1]), states)
+		id2 = findfirst(==(spec[2]), states)
+		if success[1]
+			push!(connection_strings, connects(solution_name, id1, id2))
+		end
+
+		if success[2]
+			push!(connection_strings, connects(solution_name, id2, id1))
+		end
+	end
+
+	return connection_strings
+end
+
+# ╔═╡ 5840a8e6-1451-4637-9099-2256246baeb3
+@assert length(states) > 0
+
+# ╔═╡ 070c8187-736d-4fe6-adbd-923e38d4f731
+states
+
+# ╔═╡ 56fb75e5-f3ae-47af-a425-a92c784087a6
+zip(vertex_names, eachcol((hcat(states...)')))
+
+# ╔═╡ ac6532ec-3bd6-46e0-9ca9-8b3f18006fd3
+permutedims(DataFrame(zip(vertex_names, eachcol((hcat(states...)')))), 1)
+
+# ╔═╡ b917a2ab-f41a-45ff-83a4-60cb43c9feb3
+sol_ids = [df.exprs_and_scores[i] .|> (x -> x[4]) for i in eachindex(df.exprs_and_scores)]
+
+# ╔═╡ e495d254-df86-4ff4-9c3c-cfcbf8c8781e
+length.(sol_ids)
+
+# ╔═╡ 691e4ff4-177a-4a12-b353-6cfc2b4180be
+solution_names_stacked =  [["$(vertex_names[vert])_$id" for id in sol_ids[vert]] for vert in eachindex(vertex_names)]
+
+# ╔═╡ 1996288a-5696-4d59-ab5f-f8f64dae1954
+solution_names = solution_names_stacked |> Iterators.flatten |> collect
+
+# ╔═╡ 356f324b-43bc-4f55-8c59-1582e35daf57
+solution_strings = ["solution($x)." for x in solution_names]
+
+# ╔═╡ 129079df-3878-4534-bd53-309dc3dea2bf
+md"""
+### Solution Pruning
+
+While we have $(length(solution_strings)) solutions, many of these solutions induce the same topology within the state space. If we only take the first (simplest) solution for each induced topology, we create much fewer constants for Clingo to work with, speeding up the grounding and possibly also the solving process. The per-transition successes show the topology each solution induces in the state space, so we can filter on unique values there.
+"""
+
+# ╔═╡ 20ea6a2d-bf12-4233-b142-14fcd6771ef3
+@assert all(split.(solution_names, '_') .|> first |> unique .|> (x -> x in vertex_names))
+
+# ╔═╡ 2235412f-48b1-4e85-915d-d2d37b2feabc
+@assert all(split.(solution_names, '_') .|> last |> unique |> Iterators.flatten .|> isdigit)
+
+# ╔═╡ 8f09510b-c354-4061-bbb4-c5c69a7e17fb
+@assert all(in.('_', solution_names))
+
+# ╔═╡ 52d6f600-0c64-40f3-a171-dab105bcb9fc
+@assert all(length.(split.(solution_names, '_')) .== 2)
+
+# ╔═╡ b8ae91eb-be7e-4794-9fdf-4379a7c6b9df
+solution_names_stacked
+
+# ╔═╡ b45ae1e4-00f7-4648-9048-432f52d1ab3b
+sol_exprs_printable = [df.exprs_and_scores[i] .|> (x -> x[1]) for i in eachindex(df.exprs_and_scores)][1][999] |> string |> x -> replace(x, "SoleLogics.Atom{SubString{String}}: v_" => "")
+
+# ╔═╡ 1c555d75-fa37-493f-9a6b-14bba03924da
+pertransition_successes = [df.exprs_and_scores[i] .|> (x -> x[3]) for i in eachindex(df.exprs_and_scores)]
+
+# ╔═╡ f561ee12-0bb4-476e-9873-9b0504282321
+n_successes = length.(pertransition_successes)
+
+# ╔═╡ 963c1b25-d58a-4823-aa58-5c68e5c3bb8a
+md"""
+Unfiltered, we see that we have $(join(n_successes, ", ", " and ")) solutions for each of the 5 nodes in the model.
+"""
+
+# ╔═╡ e79fe49c-1307-46ce-ac8e-f8a785f40e6a
+unique_successes = pertransition_successes .|> unique
+
+# ╔═╡ c379dbbe-5cdc-494e-9228-81be16c3a2d1
+n_unique_successes = length.(unique_successes)
+
+# ╔═╡ 191f4126-95a6-4686-a898-0f28b2a67352
+sum(n_unique_successes)
+
+# ╔═╡ 7052b305-fc5f-4277-9ef2-b27f817350c4
+md"""
+However, after filtering out unique values, we end up with only $(join(n_unique_successes, ", ", " and ")) for each!
+"""
+
+# ╔═╡ afcd3d60-5be0-46dd-ba09-ae2fc7089059
+unique_indices = [unique(i -> x[i], eachindex(x)) for x in pertransition_successes]
+
+# ╔═╡ 459a1a38-f0d2-41b2-9e10-38ed10caa135
+solution_names_filtered_and_stacked = filtered ? [solutions[idxs] for (solutions, idxs) in zip(solution_names_stacked, unique_indices)] : solution_names_stacked
+
+# ╔═╡ 29c3b786-82bd-40e7-bb1d-0aa1f3e7921d
+solution_names_filtered = solution_names_filtered_and_stacked |> Iterators.flatten |> collect
+
+# ╔═╡ 80d449f8-13ea-40d4-b3bd-58ca766a15ae
+solution_strings_filtered = ["solution($x)." for x in solution_names_filtered]
+
+# ╔═╡ 36d8a531-a6c2-49eb-95ed-741c16b76209
+solution_strings_filtered
+
+# ╔═╡ 065f36d0-ea7e-4eb7-a82c-5236c3df0044
+belongs_to_strings = ["belongs_to($(entity)_$id, $entity)." for (entity, id) in split.(solution_names_filtered, "_")]
+
+# ╔═╡ e6f5276e-5660-435a-a151-8af927b0c301
+belongs_to_strings
+
+# ╔═╡ feb6c350-5eb9-462d-8ba9-6185fe97441c
+@assert all(in.(assignments, (solution_names_filtered,)))
+
+# ╔═╡ c56a5fa7-18e9-4257-9bea-b85e51faeaca
+sol_idxs = [only(findall(==(assignments[i]), solution_names_filtered_and_stacked[i])) for i in eachindex(assignments)]
+
+# ╔═╡ 52f6ab50-9c4f-41b4-b9f7-8a47cdad6c42
+@assert filtered ? (solution_names_filtered |> length) == (pertransition_successes |> Iterators.flatten |> unique |> length) : true
+
+# ╔═╡ 982b0fab-1eee-4231-a656-557484fb0aaf
+pertransition_successes |> Iterators.flatten |> Iterators.flatten |> Iterators.flatten |> count
+
+# ╔═╡ 08f84a71-db13-47ff-8144-d6879fd7cb3c
+pertransition_successes .|> unique |> Iterators.flatten |> collect 
+
+# ╔═╡ 28af4ee4-0fb6-4377-b17d-ed1e8d1d3598
+pertransition_successes |> Iterators.flatten |> collect 
+
+# ╔═╡ 97c803c6-00c0-42e0-9c97-ff015a51335c
+pertransition_successes |> Iterators.flatten .|> unique |> collect 
+
+# ╔═╡ 8b570775-6afe-435d-b3f6-4030b0df5e6c
+sol_trans = [pertransition_successes[i][sol_idxs[i]] for i in eachindex(sol_idxs)]
+
+# ╔═╡ 56e58ef6-e48f-4971-ba3b-e88a0957b4c7
+first_transition in (pertransition_successes |> Iterators.flatten |> unique)
+
+# ╔═╡ 49112c99-533c-4f96-acfe-1f660df01d74
+df.selected_trajectories .|> first
+
+# ╔═╡ 2ba7e499-44e0-435d-8f2f-dba92a7270fe
+foreach(x -> println(x), df.selected_trajectories[1])
+
+# ╔═╡ 9fe9fae0-ef94-4b40-89ea-32eb314013d0
+sol_connections = [df.exprs_and_scores[i] .|> (x -> x[3]) for i in eachindex(df.exprs_and_scores)]
+
+# ╔═╡ 414b38e6-c0c1-4429-907e-a7f836f5312c
+trajectories = [df.selected_trajectories[i] .|> collect for i in eachindex(df.selected_trajectories)]
+
+# ╔═╡ 072404b8-a243-4b40-86ea-52393754de4f
+raw_connections_stacked = [[raw_connection_builder(name[i], conn[i], traj) for i in eachindex(name)] for (name, conn, traj) in zip(solution_names_filtered_and_stacked, sol_connections, trajectories)]
+
+# ╔═╡ 4a4190e7-6c01-47b6-801c-97b3f3165050
+raw_connections_stacked |> Iterators.flatten |> Iterators.flatten |> collect |> length
+
+# ╔═╡ 75257860-f733-441f-95ee-93c6d1b7ae2a
+connection_strings_stacked = [[connection_builder(name[i], conn[i], traj) for i in eachindex(name)] for (name, conn, traj) in zip(solution_names_filtered_and_stacked, sol_connections, trajectories)]
+
+# ╔═╡ 56448558-2952-4764-8766-36e8c62d1de5
+connection_strings = connection_strings_stacked |> Iterators.flatten |> Iterators.flatten |> collect
+
+# ╔═╡ caf5fbec-f323-45ed-94c9-bfd0957ff97c
+connection_strings
+
+# ╔═╡ b563aa33-ee26-4c12-98f6-65d02cd3899d
+mktemp() do path, io
+	println(io, entity_string)
+	println(io, state_string)
+	for x in solution_strings_filtered
+		println(io, x)
+	end
+	println(io, steady_state_string)
+	for x in belongs_to_strings
+		println(io, x)
+	end
+	for x in connection_strings
+		println(io, x)
+	end
+	println(io, model_def)
+	close(io)
+	# @show length(readlines(path))
+	
+	# @benchmark
+	run(pipeline(ignorestatus(`$(Clingo_jll.clingo()) -n10000 $path`))) 
+	# setup=(path=$path)
+end
+
+# ╔═╡ 25dd6bf1-4ca2-4084-b682-858020d90bbc
+sol_exprs = [df.exprs_and_scores[i] .|> (x -> x[1]) for i in eachindex(df.exprs_and_scores)]
+
+# ╔═╡ d5b485db-6b4d-4ede-ae64-bf8448451ddf
+selected_exprs = [sol_exprs[i][sol_idxs[i]] for i in eachindex(sol_idxs)]
+
+# ╔═╡ Cell order:
+# ╟─f09edd39-ffeb-4850-b29e-b38565273ff5
+# ╟─c081cd85-b5af-4208-9ca8-90e2b1c02d0f
+# ╠═4f017c2b-7f3d-4ff8-95ba-6581c55ee5f3
+# ╠═ed8ac9f3-e361-4e05-a160-bbb5e3c2b2a1
+# ╟─701cca9d-f8de-4160-8f5d-c1ce30d31525
+# ╟─e1421a5b-11c7-44a8-b6f0-4654489a2b81
+# ╟─8a2c00df-b9a9-42a2-ac0c-e243527545af
+# ╠═1c9ab992-a1d4-4a03-af70-358389149f15
+# ╟─690734ed-bdbf-4635-a4d2-37500fcea3cf
+# ╠═b917a2ab-f41a-45ff-83a4-60cb43c9feb3
+# ╠═b45ae1e4-00f7-4648-9048-432f52d1ab3b
+# ╠═e495d254-df86-4ff4-9c3c-cfcbf8c8781e
+# ╠═691e4ff4-177a-4a12-b353-6cfc2b4180be
+# ╠═1996288a-5696-4d59-ab5f-f8f64dae1954
+# ╠═356f324b-43bc-4f55-8c59-1582e35daf57
+# ╟─129079df-3878-4534-bd53-309dc3dea2bf
+# ╠═b8ae91eb-be7e-4794-9fdf-4379a7c6b9df
+# ╟─1c555d75-fa37-493f-9a6b-14bba03924da
+# ╟─f561ee12-0bb4-476e-9873-9b0504282321
+# ╟─963c1b25-d58a-4823-aa58-5c68e5c3bb8a
+# ╠═e79fe49c-1307-46ce-ac8e-f8a785f40e6a
+# ╟─c379dbbe-5cdc-494e-9228-81be16c3a2d1
+# ╠═191f4126-95a6-4686-a898-0f28b2a67352
+# ╟─7052b305-fc5f-4277-9ef2-b27f817350c4
+# ╠═afcd3d60-5be0-46dd-ba09-ae2fc7089059
+# ╠═459a1a38-f0d2-41b2-9e10-38ed10caa135
+# ╠═29c3b786-82bd-40e7-bb1d-0aa1f3e7921d
+# ╠═80d449f8-13ea-40d4-b3bd-58ca766a15ae
+# ╟─51f9d1b9-304e-417f-9925-b572a90e278e
+# ╟─f298831c-8954-4957-a2b9-92f7b0cf9ca7
+# ╟─b8265bb9-83d4-4bfd-9480-a9b55d78495e
+# ╠═437a480c-e63d-40f2-9d01-dd95275a333c
+# ╠═7e86270e-0faf-4b05-b5b2-f446d62e3320
+# ╠═003f7d18-1801-4eda-9092-1d8685e41da6
+# ╠═cf9bb61c-7892-4b0b-91fe-e9c437be849d
+# ╠═e699ff65-d7cc-4a9b-80b8-1fe4b17bb6ea
+# ╠═49112c99-533c-4f96-acfe-1f660df01d74
+# ╠═38bcaaaf-5ddb-4536-b270-4b93caba66c2
+# ╠═17aa2324-3b02-47c9-8c91-9bbdd4c3cb4a
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diff --git a/experiments/Synth/notebooks/march_2025_presentation.jl b/experiments/Synth/notebooks/march_2025_presentation.jl
new file mode 100644
index 0000000..a2ff728
--- /dev/null
+++ b/experiments/Synth/notebooks/march_2025_presentation.jl
@@ -0,0 +1,778 @@
+### A Pluto.jl notebook ###
+# v0.20.4
+
+using Markdown
+using InteractiveUtils
+
+# ╔═╡ b6578081-a6fe-4637-903e-4435f7e6c749
+using DrWatson
+
+# ╔═╡ d03d06ee-5614-4fdd-889d-48c8710b261c
+begin
+	quickactivate(@__DIR__)
+	using Revise
+	using GraphDynamicalSystems
+	using Synth
+	using Herb
+	using MetaGraphsNext: labels
+	import MetaGraphsNext
+	using SoleLogics: value, Atom
+	# using ProgressMeter, DataFrames, HerbSearch, Random
+	using MetaGraphsNext: labels
+	# using Statistics: quantile
+	# using DynamicalSystems
+	using Clingo_jll
+	using Plots
+	using Graphs
+	using GraphRecipes
+	using PlutoUI
+	# using Herb
+	using SoleLogics
+	using MLStyle
+	import HerbConstraints.pattern_match
+	using HerbConstraints: PatternMatchResult, PatternMatchSuccess, PatternMatchSoftFail, PatternMatchHardFail, PatternMatchSuccessWhenHoleAssignedTo
+end
+
+# ╔═╡ fa93f89e-05ab-11f0-2dfe-f1e019d9bfe8
+html"""
+<h1></h1>
+<div id="titlebox">
+<p class="noborder">
+<span class="gone">Synthesizing</span> 
+<span class="verylight"><i>Networks of State Machines</i></span>
+</p>
+<p class="noborder">
+<span class="gone">Synthesizing</span> 
+<span class="light"><i>Dynamical Systems</i></span>
+</p>
+
+<p style="border-bottom: none">Synthesizing <i>Biological Models</i></p>
+<p class="noborder">
+<span class="gone">Synthesizing</span> 
+<span class="light"><i>Qualitative Networks</i></span>
+</p>
+<p class="noborder">
+<span class="gone">Synthesizing</span> 
+<span class="verylight"><i>Boolean Networks</i></span>
+</p>
+</div>
+
+<div style="text-align: center">03/26/2024 Update Meeting</div>
+
+"""
+
+# ╔═╡ a1718e12-bfdf-44fe-a930-c9131e64d144
+md"""
+## Agenda
+
+1. Unified formulation of the synthesis problem
+2. What we have
+3. What we're missing
+4. Questions
+"""
+
+# ╔═╡ 3e8e48cc-790c-4a18-990a-637372d432d2
+md"""
+## Synthesis Problem Formulation
+
+Given:
+
+- A *grammar* for target functions (arithmetic for QNs, logical operators for BNs)
+  - Includes a set of *genes/proteins*
+- A *specification*, which is one or both of
+  - *Longitudinal data*: state transition pairs and steady states
+  - *Perturbation data*: fixed values for a subset of genes/proteins, and steady states
+
+
+Find:
+
+- A set of *target functions* for each gene/protein
+- Satisfying combinations of target functions must match the specification's
+  - Steady states (under perturbation as well, if given)
+  - State transition pairs, if given
+"""
+
+# ╔═╡ 1b53d4e4-fb36-4c8a-9e35-55c3832f0005
+md"""
+### Formulation Examples
+
+!!! tip "Target Functions"
+	Set of functions, one per gene/protein
+	```julia
+	Coup_fti = ...
+	Emx2 = Coup_fti / (1 - Fgf8)
+	Fgf8 = ...
+	```
+	When assembled into a complete model (QN, for example), a satisfying set of functions should match the specification (longitudinal and/or perturbation)
+"""
+
+# ╔═╡ ef9ea3aa-1022-409e-8b6e-d79e0455bfc8
+md"""
+## ✓ What we have
+
+A synthesis pipeline that starts either from
+
+- An existing model, sampling longitudinal data, and steady state(s) from it
+- Longitudinal data and steady state(s) directly
+
+and synthesizes a set of target functions whose combination matches the longitundal data and steady states.
+
+The pipeline:
+
+1. Constructs a grammar for the problem
+2. Enumerates candidate functions from the grammar
+3. Checks candidate functions against the longitudinal data (state transition pairs)
+4. Uses the result to select possible combinations of target functions that have the specified steady state(s)
+"""
+
+# ╔═╡ f00faa20-d261-433d-908e-8047b5a5d45a
+md"""
+### Walk through
+
+1. The model we start with
+2. Sampling data from it
+3. Synthesizing possible target functions
+4. Combining to a complete model
+"""
+
+# ╔═╡ df82d6bc-2c8b-48ec-b4fc-7d0c0ce9d7d3
+md"""
+#### Original Model
+"""
+
+# ╔═╡ f38f30d0-c875-4f1a-819d-a4b20cb382ff
+md"""
+!!! info ""
+	Giacomantonio CE, Goodhill GJ (2010) A Boolean Model of the Gene Regulatory Network Underlying Mammalian Cortical Area Development. PLoS Comput Biol 6(9): e1000936. [https://doi.org/10.1371/journal.pcbi.1000936](https://doi.org/10.1371/journal.pcbi.1000936)
+"""
+
+# ╔═╡ a03aab2a-8af1-4c0c-aae7-ef34b96c1702
+begin
+	n_trajectories = 10
+	length_trajectory = 10
+	max_iterations = 50000
+	max_depth = 3
+end
+
+# ╔═╡ 4710d9e8-7781-4b01-bec5-c8e30219b5c2
+s1 = [0, 0, 1, 1, 1]
+
+# ╔═╡ 648ddc71-f6f3-44ac-b44a-8d0f1a5ed958
+s2 = [1, 0, 1, 1, 1]
+
+# ╔═╡ fd621392-67d6-4b3d-beb7-04c963f5b993
+searching = Set([s1, s2])
+
+# ╔═╡ 9dc68992-7f48-4ed7-af1e-61bc6d693f8c
+md"""
+### Combining Local Solutions
+
+→ Other notebook
+"""
+
+# ╔═╡ d4604287-fde2-4fc9-961b-4505e8210551
+md"""
+## ❗ What we're missing
+
+- Current models will definitely enter all steady states, but might enter other steady states outside of the specification
+  - Next step is to verify this
+"""
+
+# ╔═╡ 426f51b8-c9ec-42e9-8d21-9573183f48f4
+md"""
+## ❓ Questions
+
+- When *you* use BMA, what do you verify?
+  - If something is wrong, how do you use the outcome of the verification to fix it?
+- What does model stabilization mean to you?
+  - Do oscillating states count?
+- Can we assume we have all steady states present in the data?
+- When working with perturbation data, what can we start from as a target function?
+- Any patterns of target functions that you often see?
+- Current approach can create “correct” models that visit states that were not in the data
+  - Do we want to minimize this?
+  - For example, which one to choose?
+    - We have a simple model that visits many states not in the data, but has the correct dynamics
+    - We have a complex model that stays within the states in the data
+- Which specific papers to re-do?
+
+"""
+
+# ╔═╡ cdc9908c-d858-4cee-ac08-2b135e8aabd2
+md"""
+# Appendix
+"""
+
+# ╔═╡ f9e3c41e-1ab9-4a58-aaad-5c97c888728c
+md"""
+## Data Loading
+"""
+
+# ╔═╡ 48bf71ae-ca36-40aa-a65f-e7eb37953058
+begin
+	model_df = collect_results(datadir("src_parsed", "biodivine_benchmark_as_metagraphs"););
+	path2id = path -> parse(Int, splitext(basename(path))[1])
+	model_df.ID = path2id.(model_df.path)
+	model007 = only(model_df[model_df.ID .== 7, :metagraph_model])
+end
+
+# ╔═╡ 86faab19-6712-4d7e-aeb8-1ea1febc3b97
+original_model_plot = plot(reverse(model007.graph); names=labels(model007) .|> string .|> (x -> x[39:end]), method=:shell, self_edge_size=0.12, nodecolor=:white, nodeshape=:circle)
+
+# ╔═╡ 9551231b-753d-4958-8444-23cbdae1146e
+savefig(original_model_plot, "original_model_plot.png")
+
+# ╔═╡ fe8fbd0b-c384-4d93-ab5a-230d67ec6f8f
+functions007 = Pair.(labels(model007) .|> string .|> (x -> x[39:end]), (labels(model007) .|> (x -> model007[x]) .|> string .|> (x -> x[26:end]) .|> (x -> replace(x, "v_" => "")))) |> Dict;
+
+# ╔═╡ ad6776d9-6fec-467a-a75e-c0ec86afdaf9
+md"""
+$(Markdown.Table([["Gene", "Target Function"], [[k, v] for (k, v) in functions007]...], [:l, :l]))
+"""
+
+# ╔═╡ 94d4c053-c02e-4a07-93b2-63438759acb8
+begin
+	trajectories = []
+	for i in 1:n_trajectories
+		abn7 = BooleanNetworks.abn(model007; seed=i)
+		data = gather_bn_data(abn7, length_trajectory)
+		push!(trajectories, data)
+	end
+	states = trajectories |> Iterators.flatten |> unique
+end
+
+# ╔═╡ 2abbdd40-8e4e-49d6-ad5a-ecfa46c588d8
+for s in states
+	print("[], ")
+	for x in s
+		print("[$x], ")
+	end
+	println()
+end
+
+# ╔═╡ 754c499a-28e3-42fb-bed3-e466ed1c7393
+begin
+	io_pairs = []
+	for (i, s) in enumerate(states)
+		adjacents = states .- (s,) .|> (x -> abs.(x)) .|> sum .|> ==(1)
+
+		for other_state in states[adjacents]
+			push!(io_pairs, (s, other_state))
+		end
+	end
+	io_pairs
+end
+
+# ╔═╡ b21cb05c-f72e-411f-a2fd-b675e84e23b7
+md"""
+### Formulation Examples
+
+$(Markdown.Admonition("tip", "Specification: Longitudinal Data", [
+	Markdown.Paragraph("State transition pairs such as"),
+	Markdown.Code("julia", join(string.(io_pairs[1:3]), "\n") * "\n..."),
+	Markdown.Paragraph("With one or more of these states marked as steady"),
+]))
+
+!!! warning "Specification: Perturbation Data"
+	Fixed value, and a corresponding steady state
+
+	```julia
+	[□, □, □, 1, □] → [0, 0, 1, 1, 0]
+	```
+
+	`□`: unfixed value
+
+"""
+
+# ╔═╡ 282c25ec-8847-4ca9-bee9-7b9d0874c2b8
+begin
+	state_space = MetaGraphsNext.MetaGraph(SimpleGraph(), label_type=AbstractVector)
+	add_vertex!.((state_space,), states)
+	[add_edge!(state_space, x[1], x[2]) for x in io_pairs]
+end
+
+# ╔═╡ 7a67e9fe-7bf9-4117-8e00-10afcee2f239
+state_space_plot = plot(state_space.graph, curves=false, method=:stress)
+
+# ╔═╡ f2c73222-3c36-415a-97ae-b8a1a15b574f
+savefig(state_space_plot, "state_space.png")
+
+# ╔═╡ 91f44e97-bbac-413d-8331-dc1328f96f89
+md"""
+### Converting to IO Pairs
+
+Then, we convert to input/output pairs to check the target functions. In this case, we are assuming an asynchronous update schedule, so every pair of states that is a hamming distance of 1 apart becomes an example.
+
+$(Markdown.Code("julia", join(string.(io_pairs[1:3]), "\n") * "\n..."))
+
+"""
+
+# ╔═╡ cd238a3a-d6a3-464b-a249-d2e66236ee50
+unique_transitions = io_pairs .|> Set |> unique .|> collect
+
+# ╔═╡ e4732348-0188-4fb0-a0cd-e1888ec5f9fd
+state_string = "state(1..$(length(states)))."
+
+# ╔═╡ 911de256-b75e-4503-9702-c70e70be5779
+entity_names = model007 |> labels .|> value .|> (x -> replace(x, "v_" => "")) .|> Symbol
+
+# ╔═╡ d42cbcbd-5990-4818-9edb-02d631486667
+md"""
+### Sampling Longitudinal Data
+
+Data comes as a set of states. Each row here is a state.
+
+$(Markdown.Table([["Gene", string.(entity_names)...], [vcat("", s) for (i, s) in enumerate(states)]...], [:l, :l, :l, :l, :l, :l]))
+
+"""
+
+# ╔═╡ 2cf1d0f3-5f6f-4fd7-ac97-9072f25f9917
+problems = [
+	UndirectedProblem(
+		string(entity_names[i]),
+		[
+			UndirectedExample(
+				Dict(:state => t[1]),
+				Dict(:state => t[2])
+			) for t in unique_transitions if t[1][i] != t[2][i]
+		]
+	) for i in 1:length(entity_names)
+]
+
+# ╔═╡ 8e075539-3c74-4506-9191-74c0c2944d94
+[Set([x.data1[:state], x.data2[:state]]) for x in problems[1].examples]
+
+# ╔═╡ 5ccb2ec7-b0ee-48de-9acc-a44de5ddb57d
+problems[1].examples
+
+# ╔═╡ 9fece869-b636-410e-a480-9f5fcbec5a75
+entity_string = "entity($(join(entity_names, ";")))."
+
+# ╔═╡ a6657d7d-0bc3-4c83-bbef-c43e519d6cb4
+base_grammar_string = let io = IOBuffer()
+	Base.show(io, GraphDynamicalSystems.base_qn_grammar)
+	String(take!(io))
+end
+
+# ╔═╡ 9925d04e-e042-4d14-ad37-bba85aa54a34
+md"""
+### Formulation Examples
+
+$(Markdown.Admonition("info", "Grammar", [
+	Markdown.Paragraph("QN grammar, matching the BMA tool"),
+	Markdown.Code("julia", base_grammar_string),
+	Markdown.Paragraph("In a full grammar, we also have `Val = Gene/Protein` for each one in the problem"),
+]))
+"""
+
+# ╔═╡ e6fdb952-424a-492f-b9a4-01984a4824bb
+function build_qn_grammar(
+    entity_names,
+    constants = default_qn_constants,
+)
+    g = deepcopy(GraphDynamicalSystems.base_qn_grammar)
+	n_original_rules = length(g.rules)
+	n_entities = length(entity_names)
+	
+    for e in entity_names
+        add_rule!(g, :(Val = $e))
+    end
+
+    for c in constants
+        add_rule!(g, :(Val = $c))
+    end
+
+	original_rules_domain = BitVector(zeros(length(g.rules)))
+	original_rules_domain[[1:n_original_rules...]] .= true
+	entity_domain = BitVector(zeros(length(g.rules)))
+	entity_domain[[n_original_rules+1:n_original_rules + n_entities...]] .= true
+	constants_domain = .~(entity_domain .| original_rules_domain)
+
+    # +, *, min, max, are all commutative
+	domain = BitVector(zeros(length(g.rules)))
+	@. domain[[1, 4:6...]] = true
+    template_tree = DomainRuleNode(domain, [VarNode(:a), VarNode(:b)])
+    order = [:a, :b]
+
+    addconstraint!(g, Ordered(template_tree, order))
+
+    # Forbid same arguments for 2-argument functions
+	domain = BitVector(zeros(length(g.rules)))
+	@. domain[length(g.childtypes) == 2] = true
+    template_tree = DomainRuleNode(domain, [VarNode(:a), VarNode(:a)])
+
+    addconstraint!(g, Forbidden(template_tree))
+
+    # Forbid Ceil and Floor from including an entity or constant directly
+	domain = BitVector(zeros(length(g.rules)))
+	domain[[n_original_rules+1:length(g.rules)...]] .= true
+	
+    entities_consts = DomainRuleNode(domain)
+	
+	domain = BitVector(zeros(length(g.rules)))
+	domain[[7, 8]] .= true
+	
+    template_tree = DomainRuleNode(domain, [entities_consts])
+
+    addconstraint!(g, Forbidden(template_tree))
+
+    # Forbid ceil(floor(x)) and vice-versa
+	ceil_or_floor = BitVector(zeros(length(g.rules)))
+    ceil_or_floor[[7, 8]] .= true
+    template_tree =
+        DomainRuleNode(ceil_or_floor, [DomainRuleNode(ceil_or_floor, [VarNode(:a)])])
+
+    addconstraint!(g, Forbidden(template_tree))
+
+	# Forbid constants as numerator of /
+	addconstraint!(g, Forbidden(RuleNode(3, [
+		DomainRuleNode(constants_domain),
+		VarNode(:a)
+	])))
+
+	# Force programs to reference at least one entity
+	addconstraint!(g, ContainsSubtree(DomainRuleNode(entity_domain)))
+
+	# Forbid programs to add or subtract 0
+	# zero_index = only(findall(g.rules .== (:(0),)))
+	# add_subtract_domain = (g.rules .== (:(Val + Val),)) .| (g.rules .== (:(Val - Val),))
+	# addconstraint!(g, Forbidden(DomainRuleNode(add_subtract_domain, [VarNode(:a), RuleNode(zero_index)])))
+
+	# Forbid programs to multiply by 0 or 1
+	zero_one_domain = (g.rules .== (:(0),)) .| (g.rules .== (:(1),))
+	multiply_index = only(findall((g.rules .== (:(Val * Val),))))
+	addconstraint!(g, Forbidden(RuleNode(multiply_index, [VarNode(:a), DomainRuleNode(zero_one_domain)])))
+
+	# Forbid division by 0 or 1
+	zero_domain = (g.rules .== (:(0),)) .| (g.rules .== (:(1),))
+	division_index = only(findall((g.rules .== (:(Val / Val),))))
+	addconstraint!(g, Forbidden(RuleNode(division_index, [VarNode(:a), DomainRuleNode(zero_domain)])))
+	
+	# Forbid min and max
+	# min_max_domain = (g.rules .== (:(Min(Val, Val)),)) .| (g.rules .== (:(Max(Val, Val)),))
+	
+	# addconstraint!(g, Forbidden(DomainRuleNode(min_max_domain, [VarNode(:a), VarNode(:b)])))
+
+	# Forbid both constants for 2-argument functions
+	domain = BitVector(zeros(length(g.rules)))
+	@. domain[length(g.childtypes) == 2] = true
+    template_tree = DomainRuleNode(domain, [
+		DomainRuleNode(constants_domain),
+		DomainRuleNode(constants_domain)
+	])
+
+	addconstraint!(g, Forbidden(template_tree))
+
+	# * by 1
+
+    return g
+end
+
+# ╔═╡ 5aebfdef-39d4-431e-826b-3039c95af013
+grammar = build_qn_grammar(
+	entity_names,
+	[1]
+)
+
+# ╔═╡ 21ebebde-1794-47e2-a3cb-d1b78bff2c6e
+function make_iter()
+	return Herb.BFSIterator(grammar, :Val; max_depth)
+end
+
+# ╔═╡ fcb30d9c-ca63-4a9d-8b64-a178fdba50a7
+total_number_progs_possible = begin
+	iter = make_iter()
+	length(iter)
+end
+
+# ╔═╡ f8e7784b-e706-4ac8-8373-f60566a30ddc
+grammar_string = let io = IOBuffer()
+	Base.show(io, grammar)
+	String(take!(io))
+end
+
+# ╔═╡ cb24a482-5323-4a3d-b03b-6a8d4b9a6183
+md"""
+### Enumerating Candidate Functions
+
+From our grammar
+
+$(Markdown.Code("julia", grammar_string))
+
+We enumerate all programs up to a certain depth (which is $total_number_progs_possible in total, in this case)
+
+We apply a number of constraints in the enumeration process to prune many possible functions.
+
+- +, *, min, max, are all commutative
+- Forbid same arguments for 2-argument functions
+- Forbid division by 1
+- Forbid only constants for 2-argument functions
+- Forbid `ceil` and `floor` from including a gene or constant directly
+- Forbid `ceil(floor(x))` and vice-versa
+- Forbid constants as numerator of /
+
+"""
+
+# ╔═╡ e94f29d0-ea06-4678-86b4-3481db701c9d
+function Synth.synth_biodivine(
+    problem,
+    iterator,
+    grammar,
+    max_iterations,
+    evaluator,
+    vertex_names,
+)
+    exprs_and_scores = []
+
+    for (i, ex) in enumerate(iterator)
+        if i % 100000 == 0
+            @info "$i iterations, problem $(problem.name)"
+        end
+
+        expr = rulenode2expr(ex, grammar)
+
+        sat_examples = nothing
+        try
+            sat_examples = evaluator(problem, expr, vertex_names)
+        catch e
+            @error "Problem evaluating: Problem name $(problem.name), expr: $expr, i: $i."
+            rethrow(e)
+        end
+
+        if isnothing(sat_examples)
+            push!(exprs_and_scores, (expr, nothing, nothing, i))
+            # if all examples worked in at least one direction
+        elseif sum(all.(==(false), sat_examples)) == 0
+            score = sum(count.(sat_examples)) / (2 * length(problem.examples))
+            push!(exprs_and_scores, (expr, score, sat_examples, i))
+        end
+
+        if i > max_iterations
+            @warn "Maximum iterations reached"
+            break
+        end
+    end
+
+    return exprs_and_scores
+end
+
+# ╔═╡ 938bcef0-2e9d-43bf-9886-c012034453dc
+function interpret_qn(
+    e,# ::Union{AbstractString,Integer,Expr,Atom},
+    qn_state, #::AbstractVector{<:Integer},
+    vertex_names #::AbstractVector{<:AbstractString},
+)
+    state_map = Dict(zip(vertex_names, deepcopy(qn_state)))
+
+    _int(e) = @match e begin
+        ::AbstractString => state_map[e]
+        ::Atom => state_map[e]
+        ::Integer => e
+		::Symbol => state_map[string(e)]
+        :($v1 + $v2) => _int(v1) + _int(v2)
+        :($v1 - $v2) => _int(v1) - _int(v2)
+        :($v1 / $v2) => _int(v1) / _int(v2)
+        :($v1 * $v2) => _int(v1) * _int(v2)
+        :(Min($v1, $v2)) => min(_int(v1), _int(v2))
+        :(Max($v1, $v2)) => max(_int(v1), _int(v2))
+        :(Ceil($v)) => ceil(_int(v))
+        :(Floor($v)) => floor(_int(v))
+        _ => error("Unhandled Expr in `interpret`: $e, $(typeof(e))")
+    end
+
+    return _int(e)
+end
+
+# ╔═╡ 62e4af8c-b1cc-428b-981c-f5600f65b714
+function Synth.evaluate_qn(problem::UndirectedProblem, expr, vertex_names)
+    sat_examples = BitVector[]
+	vertex_index = only(findall(==(problem.name), vertex_names))
+
+    function _eval_1_dir(in, out)
+        res = interpret_qn(expr, in[:state], vertex_names)
+        expected = out[:state][vertex_index]
+        success = expected == res
+        return success
+    end
+
+    for example ∈ problem.examples
+        success_direction1 = _eval_1_dir(example.data1, example.data2)
+        success_direction2 = _eval_1_dir(example.data2, example.data1)
+
+        success = BitVector([success_direction1, success_direction2])
+
+        push!(sat_examples, success)
+    end
+
+    return sat_examples
+end
+
+# ╔═╡ 3f2f2fe4-3c84-4bf0-ba7f-8168f5d840bf
+results = synth_biodivine.(
+	problems,
+	(make_iter(),),
+	(grammar,),
+	(max_iterations,),
+	(evaluate_qn,),
+	(string.(entity_names),)
+)
+
+# ╔═╡ ca878159-a262-46f4-a012-03b6f3ee3ae2
+[r for r in results[1] if r[3][1] == [false, true]][begin:begin+20] .|> (x -> x[1]) .|> string .|> (x -> println(x))
+
+# ╔═╡ c1478d13-7168-4dc0-ab2a-5e4e792f910d
+length(results[1]) - 20
+
+# ╔═╡ 06002e18-f6b4-4e69-aabf-7b8537f03c3c
+[r for r in results[1] if r[3][1] == [false, true]][begin:begin+20] .|> (x -> x[1]) .|> string .|> (x -> replace(
+	x,
+	"*" => "times",
+	"Min" => "\"Min\"",
+	"Max" => "\"Max\"",
+	(string.(entity_names) .=> ["\"$e\"" for e in entity_names])...
+)) .|> (x -> println(x))
+
+# ╔═╡ 1473d4f2-4665-43e9-91f7-5bd6e9f088cb
+println.(map(x -> string(x[1]), results[1])[1:100])
+
+# ╔═╡ 5bfbfb20-cfb3-40d4-b707-e737f527402a
+length.(results)
+
+# ╔═╡ a32ee36a-535f-44ed-997f-7d887a4e2345
+n_programs_per_entity = ["$name → $num" for (name, num) in zip(entity_names, length.(results))]
+
+# ╔═╡ 64eeefec-9129-4f07-947f-73d611ee6c1c
+md"""
+### Summary Example
+
+- Unique states (sampled): $(length(states))
+- State transition pairs (Hamming distance 1): $(length(unique_transitions))
+- \# of functions possible (max-depth: 3): $total_number_progs_possible
+- \# of functions that satisfy the transitions: $(join(n_programs_per_entity, ", ", ", and "))
+"""
+
+# ╔═╡ a31cfabd-8894-42f2-95d7-201ba06a853d
+n_programs_foreach_entity = ["$num for $name" for (name, num) in zip(entity_names, length.(results))]
+
+# ╔═╡ f58351c9-f49d-4a0a-9137-06d8c68d6251
+md"""
+### Check against IO Examples
+
+With candidate programs, and IO examples, we can check which candidate programs correctly transform input to output for each example.
+
+This reduces the number of candidate functions for each entity to $(join(n_programs_foreach_entity, ", ", ", and ")).
+
+This step also gives us the information for which *direction* each candidate function works in
+"""
+
+# ╔═╡ edd72405-6889-4cbc-9b5f-4378130b0d31
+sol_ids = [results[i] .|> (x -> x[4]) for i in eachindex(results)]
+
+# ╔═╡ 1054aa3b-4675-4054-8eb9-1ff931dcbda6
+md"""
+## Notebook Setup
+"""
+
+# ╔═╡ 00383472-8b56-4504-9f9f-2b2a737e7fb4
+TableOfContents(title="26/03/25", depth=2)
+
+# ╔═╡ bd4c5a4d-e23d-49e6-82f4-3a21f9f27119
+html"""
+<style>
+	.gone {
+		opacity: 0%;
+	}
+	.light {
+		opacity: 25%;
+	}
+	.verylight {
+		opacity: 10%;
+	}
+	.noborder {
+		border-bottom: none;
+		
+	}
+	#titlebox {
+		padding-top: 4em;
+		padding-bottom: 4em;
+	}
+	#titlebox p {
+		line-height: 0.85em;
+		font-size: 2.2rem;
+		font-weight: 700;
+		font-feature-settings:"lnum","pnum";
+		color:var(--pluto-output-h-color);
+		margin-block:1rem 0;
+		font-family:Vollkorn,Palatino,Georgia,serif;
+		font-weight:600;
+		line-height:1.25em
+	}
+</style>
+"""
+
+# ╔═╡ Cell order:
+# ╟─fa93f89e-05ab-11f0-2dfe-f1e019d9bfe8
+# ╟─a1718e12-bfdf-44fe-a930-c9131e64d144
+# ╟─3e8e48cc-790c-4a18-990a-637372d432d2
+# ╟─9925d04e-e042-4d14-ad37-bba85aa54a34
+# ╟─b21cb05c-f72e-411f-a2fd-b675e84e23b7
+# ╟─1b53d4e4-fb36-4c8a-9e35-55c3832f0005
+# ╟─ef9ea3aa-1022-409e-8b6e-d79e0455bfc8
+# ╟─f00faa20-d261-433d-908e-8047b5a5d45a
+# ╟─df82d6bc-2c8b-48ec-b4fc-7d0c0ce9d7d3
+# ╟─86faab19-6712-4d7e-aeb8-1ea1febc3b97
+# ╟─9551231b-753d-4958-8444-23cbdae1146e
+# ╟─ad6776d9-6fec-467a-a75e-c0ec86afdaf9
+# ╟─f38f30d0-c875-4f1a-819d-a4b20cb382ff
+# ╟─fe8fbd0b-c384-4d93-ab5a-230d67ec6f8f
+# ╠═d42cbcbd-5990-4818-9edb-02d631486667
+# ╠═282c25ec-8847-4ca9-bee9-7b9d0874c2b8
+# ╠═2abbdd40-8e4e-49d6-ad5a-ecfa46c588d8
+# ╠═7a67e9fe-7bf9-4117-8e00-10afcee2f239
+# ╠═f2c73222-3c36-415a-97ae-b8a1a15b574f
+# ╟─91f44e97-bbac-413d-8331-dc1328f96f89
+# ╟─cb24a482-5323-4a3d-b03b-6a8d4b9a6183
+# ╟─f58351c9-f49d-4a0a-9137-06d8c68d6251
+# ╟─64eeefec-9129-4f07-947f-73d611ee6c1c
+# ╠═a03aab2a-8af1-4c0c-aae7-ef34b96c1702
+# ╠═21ebebde-1794-47e2-a3cb-d1b78bff2c6e
+# ╠═94d4c053-c02e-4a07-93b2-63438759acb8
+# ╠═754c499a-28e3-42fb-bed3-e466ed1c7393
+# ╠═cd238a3a-d6a3-464b-a249-d2e66236ee50
+# ╠═2cf1d0f3-5f6f-4fd7-ac97-9072f25f9917
+# ╠═3f2f2fe4-3c84-4bf0-ba7f-8168f5d840bf
+# ╠═4710d9e8-7781-4b01-bec5-c8e30219b5c2
+# ╠═648ddc71-f6f3-44ac-b44a-8d0f1a5ed958
+# ╠═fd621392-67d6-4b3d-beb7-04c963f5b993
+# ╠═8e075539-3c74-4506-9191-74c0c2944d94
+# ╠═5ccb2ec7-b0ee-48de-9acc-a44de5ddb57d
+# ╠═ca878159-a262-46f4-a012-03b6f3ee3ae2
+# ╠═c1478d13-7168-4dc0-ab2a-5e4e792f910d
+# ╠═06002e18-f6b4-4e69-aabf-7b8537f03c3c
+# ╠═1473d4f2-4665-43e9-91f7-5bd6e9f088cb
+# ╠═5bfbfb20-cfb3-40d4-b707-e737f527402a
+# ╠═a32ee36a-535f-44ed-997f-7d887a4e2345
+# ╠═a31cfabd-8894-42f2-95d7-201ba06a853d
+# ╠═911de256-b75e-4503-9702-c70e70be5779
+# ╠═5aebfdef-39d4-431e-826b-3039c95af013
+# ╠═fcb30d9c-ca63-4a9d-8b64-a178fdba50a7
+# ╠═9dc68992-7f48-4ed7-af1e-61bc6d693f8c
+# ╠═9fece869-b636-410e-a480-9f5fcbec5a75
+# ╟─e4732348-0188-4fb0-a0cd-e1888ec5f9fd
+# ╠═edd72405-6889-4cbc-9b5f-4378130b0d31
+# ╟─d4604287-fde2-4fc9-961b-4505e8210551
+# ╟─426f51b8-c9ec-42e9-8d21-9573183f48f4
+# ╟─cdc9908c-d858-4cee-ac08-2b135e8aabd2
+# ╟─f9e3c41e-1ab9-4a58-aaad-5c97c888728c
+# ╠═48bf71ae-ca36-40aa-a65f-e7eb37953058
+# ╠═a6657d7d-0bc3-4c83-bbef-c43e519d6cb4
+# ╠═f8e7784b-e706-4ac8-8373-f60566a30ddc
+# ╠═e6fdb952-424a-492f-b9a4-01984a4824bb
+# ╟─e94f29d0-ea06-4678-86b4-3481db701c9d
+# ╟─938bcef0-2e9d-43bf-9886-c012034453dc
+# ╟─62e4af8c-b1cc-428b-981c-f5600f65b714
+# ╟─1054aa3b-4675-4054-8eb9-1ff931dcbda6
+# ╠═00383472-8b56-4504-9f9f-2b2a737e7fb4
+# ╠═b6578081-a6fe-4637-903e-4435f7e6c749
+# ╠═d03d06ee-5614-4fdd-889d-48c8710b261c
+# ╠═bd4c5a4d-e23d-49e6-82f4-3a21f9f27119
diff --git a/experiments/Synth/notebooks/model.lp b/experiments/Synth/notebooks/model.lp
new file mode 100644
index 0000000..54524b3
--- /dev/null
+++ b/experiments/Synth/notebooks/model.lp
@@ -0,0 +1,907 @@
+entity(sp8;emx2;coupfti;pax6;fgf8).
+state(1..21).
+solution(sp8_3).
+solution(sp8_4).
+solution(sp8_5).
+solution(sp8_24).
+solution(sp8_78).
+solution(sp8_96).
+solution(sp8_99).
+solution(sp8_128).
+solution(sp8_129).
+solution(sp8_131).
+solution(sp8_1399).
+solution(sp8_1407).
+solution(sp8_1409).
+solution(sp8_1661).
+solution(sp8_1671).
+solution(sp8_1995).
+solution(sp8_1997).
+solution(sp8_2001).
+solution(sp8_3210).
+solution(sp8_3214).
+solution(sp8_3216).
+solution(sp8_3218).
+solution(sp8_5031).
+solution(sp8_6324).
+solution(sp8_6325).
+solution(sp8_6338).
+solution(sp8_6363).
+solution(sp8_6366).
+solution(sp8_6403).
+solution(sp8_6409).
+solution(sp8_6410).
+solution(sp8_6684).
+solution(emx2_1).
+solution(emx2_3).
+solution(emx2_4).
+solution(emx2_5).
+solution(emx2_19).
+solution(emx2_28).
+solution(emx2_58).
+solution(emx2_1044).
+solution(emx2_1058).
+solution(emx2_1065).
+solution(emx2_1393).
+solution(emx2_1415).
+solution(emx2_1417).
+solution(emx2_1679).
+solution(emx2_1997).
+solution(emx2_2009).
+solution(emx2_6325).
+solution(emx2_6407).
+solution(emx2_6409).
+solution(emx2_6410).
+solution(coupfti_1).
+solution(coupfti_3).
+solution(coupfti_4).
+solution(coupfti_6).
+solution(coupfti_9).
+solution(coupfti_12).
+solution(coupfti_28).
+solution(coupfti_44).
+solution(coupfti_78).
+solution(coupfti_97).
+solution(coupfti_128).
+solution(coupfti_132).
+solution(coupfti_764).
+solution(coupfti_1057).
+solution(coupfti_1395).
+solution(coupfti_1407).
+solution(coupfti_1409).
+solution(coupfti_1596).
+solution(coupfti_1671).
+solution(coupfti_1677).
+solution(coupfti_2028).
+solution(coupfti_2216).
+solution(coupfti_2266).
+solution(coupfti_2298).
+solution(coupfti_3210).
+solution(coupfti_3214).
+solution(coupfti_3216).
+solution(coupfti_3218).
+solution(coupfti_3220).
+solution(coupfti_5031).
+solution(coupfti_6255).
+solution(coupfti_6259).
+solution(coupfti_6339).
+solution(coupfti_6342).
+solution(coupfti_6357).
+solution(coupfti_6381).
+solution(coupfti_6384).
+solution(coupfti_6385).
+solution(coupfti_6429).
+solution(coupfti_6431).
+solution(coupfti_6432).
+solution(coupfti_6436).
+solution(coupfti_6443).
+solution(coupfti_6446).
+solution(pax6_1).
+solution(pax6_3).
+solution(pax6_5).
+solution(pax6_6).
+solution(pax6_17).
+solution(pax6_21).
+solution(pax6_28).
+solution(pax6_35).
+solution(pax6_57).
+solution(pax6_136).
+solution(pax6_783).
+solution(pax6_958).
+solution(pax6_972).
+solution(pax6_1000).
+solution(pax6_1049).
+solution(pax6_1059).
+solution(pax6_1407).
+solution(pax6_1997).
+solution(pax6_2021).
+solution(pax6_2142).
+solution(pax6_2266).
+solution(pax6_6261).
+solution(pax6_6262).
+solution(pax6_6265).
+solution(pax6_6325).
+solution(pax6_6326).
+solution(pax6_6347).
+solution(pax6_6348).
+solution(pax6_6349).
+solution(pax6_6393).
+solution(pax6_6395).
+solution(pax6_6398).
+solution(fgf8_1).
+solution(fgf8_4).
+solution(fgf8_6).
+solution(fgf8_20).
+solution(fgf8_759).
+solution(fgf8_1671).
+solution(fgf8_2278).
+solution(fgf8_6362).
+solution(fgf8_6441).
+steady(20;10).
+belongs_to(sp8_3, sp8).
+belongs_to(sp8_4, sp8).
+belongs_to(sp8_5, sp8).
+belongs_to(sp8_24, sp8).
+belongs_to(sp8_78, sp8).
+belongs_to(sp8_96, sp8).
+belongs_to(sp8_99, sp8).
+belongs_to(sp8_128, sp8).
+belongs_to(sp8_129, sp8).
+belongs_to(sp8_131, sp8).
+belongs_to(sp8_1399, sp8).
+belongs_to(sp8_1407, sp8).
+belongs_to(sp8_1409, sp8).
+belongs_to(sp8_1661, sp8).
+belongs_to(sp8_1671, sp8).
+belongs_to(sp8_1995, sp8).
+belongs_to(sp8_1997, sp8).
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+connects(coupfti_2266, 13, 17).
+connects(coupfti_2266, 18, 4).
+connects(coupfti_2298, 8, 15).
+connects(coupfti_2298, 11, 6).
+connects(coupfti_2298, 10, 16).
+connects(coupfti_2298, 14, 2).
+connects(coupfti_2298, 13, 17).
+connects(coupfti_2298, 4, 18).
+connects(coupfti_3210, 15, 8).
+connects(coupfti_3210, 11, 6).
+connects(coupfti_3210, 10, 16).
+connects(coupfti_3210, 14, 2).
+connects(coupfti_3210, 13, 17).
+connects(coupfti_3210, 4, 18).
+connects(coupfti_3214, 15, 8).
+connects(coupfti_3214, 11, 6).
+connects(coupfti_3214, 10, 16).
+connects(coupfti_3214, 14, 2).
+connects(coupfti_3214, 13, 17).
+connects(coupfti_3214, 4, 18).
+connects(coupfti_3216, 15, 8).
+connects(coupfti_3216, 11, 6).
+connects(coupfti_3216, 10, 16).
+connects(coupfti_3216, 14, 2).
+connects(coupfti_3216, 13, 17).
+connects(coupfti_3216, 18, 4).
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+connects(coupfti_3218, 11, 6).
+connects(coupfti_3218, 16, 10).
+connects(coupfti_3218, 14, 2).
+connects(coupfti_3218, 13, 17).
+connects(coupfti_3218, 18, 4).
+connects(coupfti_3220, 15, 8).
+connects(coupfti_3220, 6, 11).
+connects(coupfti_3220, 10, 16).
+connects(coupfti_3220, 14, 2).
+connects(coupfti_3220, 13, 17).
+connects(coupfti_3220, 4, 18).
+connects(coupfti_5031, 15, 8).
+connects(coupfti_5031, 6, 11).
+connects(coupfti_5031, 10, 16).
+connects(coupfti_5031, 2, 14).
+connects(coupfti_5031, 13, 17).
+connects(coupfti_5031, 4, 18).
+connects(coupfti_6255, 15, 8).
+connects(coupfti_6255, 6, 11).
+connects(coupfti_6255, 10, 16).
+connects(coupfti_6255, 2, 14).
+connects(coupfti_6255, 13, 17).
+connects(coupfti_6255, 4, 18).
+connects(coupfti_6259, 15, 8).
+connects(coupfti_6259, 6, 11).
+connects(coupfti_6259, 10, 16).
+connects(coupfti_6259, 14, 2).
+connects(coupfti_6259, 13, 17).
+connects(coupfti_6259, 4, 18).
+connects(coupfti_6339, 8, 15).
+connects(coupfti_6339, 11, 6).
+connects(coupfti_6339, 10, 16).
+connects(coupfti_6339, 2, 14).
+connects(coupfti_6339, 13, 17).
+connects(coupfti_6339, 18, 4).
+connects(coupfti_6342, 8, 15).
+connects(coupfti_6342, 11, 6).
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+connects(coupfti_6342, 14, 2).
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+connects(coupfti_6357, 15, 8).
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+connects(coupfti_6357, 2, 14).
+connects(coupfti_6357, 13, 17).
+connects(coupfti_6357, 18, 4).
+connects(coupfti_6381, 8, 15).
+connects(coupfti_6381, 11, 6).
+connects(coupfti_6381, 10, 16).
+connects(coupfti_6381, 2, 14).
+connects(coupfti_6381, 13, 17).
+connects(coupfti_6381, 4, 18).
+connects(coupfti_6384, 15, 8).
+connects(coupfti_6384, 11, 6).
+connects(coupfti_6384, 10, 16).
+connects(coupfti_6384, 2, 14).
+connects(coupfti_6384, 13, 17).
+connects(coupfti_6384, 18, 4).
+connects(coupfti_6385, 15, 8).
+connects(coupfti_6385, 11, 6).
+connects(coupfti_6385, 16, 10).
+connects(coupfti_6385, 2, 14).
+connects(coupfti_6385, 13, 17).
+connects(coupfti_6385, 18, 4).
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+connects(coupfti_6429, 11, 6).
+connects(coupfti_6429, 10, 16).
+connects(coupfti_6429, 2, 14).
+connects(coupfti_6429, 13, 17).
+connects(coupfti_6429, 4, 18).
+connects(coupfti_6431, 15, 8).
+connects(coupfti_6431, 11, 6).
+connects(coupfti_6431, 16, 10).
+connects(coupfti_6431, 2, 14).
+connects(coupfti_6431, 13, 17).
+connects(coupfti_6431, 18, 4).
+connects(coupfti_6432, 15, 8).
+connects(coupfti_6432, 11, 6).
+connects(coupfti_6432, 16, 10).
+connects(coupfti_6432, 2, 14).
+connects(coupfti_6432, 13, 17).
+connects(coupfti_6432, 18, 4).
+connects(coupfti_6436, 8, 15).
+connects(coupfti_6436, 11, 6).
+connects(coupfti_6436, 10, 16).
+connects(coupfti_6436, 2, 14).
+connects(coupfti_6436, 13, 17).
+connects(coupfti_6436, 4, 18).
+connects(coupfti_6443, 15, 8).
+connects(coupfti_6443, 11, 6).
+connects(coupfti_6443, 16, 10).
+connects(coupfti_6443, 2, 14).
+connects(coupfti_6443, 13, 17).
+connects(coupfti_6443, 18, 4).
+connects(coupfti_6446, 8, 15).
+connects(coupfti_6446, 11, 6).
+connects(coupfti_6446, 10, 16).
+connects(coupfti_6446, 2, 14).
+connects(coupfti_6446, 13, 17).
+connects(coupfti_6446, 4, 18).
+connects(pax6_1, 15, 13).
+connects(pax6_1, 12, 1).
+connects(pax6_1, 9, 19).
+connects(pax6_1, 2, 20).
+connects(pax6_3, 15, 13).
+connects(pax6_3, 1, 12).
+connects(pax6_3, 19, 9).
+connects(pax6_3, 2, 20).
+connects(pax6_5, 13, 15).
+connects(pax6_5, 12, 1).
+connects(pax6_5, 9, 19).
+connects(pax6_5, 20, 2).
+connects(pax6_6, 15, 13).
+connects(pax6_6, 12, 1).
+connects(pax6_6, 9, 19).
+connects(pax6_6, 20, 2).
+connects(pax6_17, 15, 13).
+connects(pax6_17, 12, 1).
+connects(pax6_17, 9, 19).
+connects(pax6_17, 2, 20).
+connects(pax6_21, 15, 13).
+connects(pax6_21, 12, 1).
+connects(pax6_21, 9, 19).
+connects(pax6_21, 2, 20).
+connects(pax6_28, 13, 15).
+connects(pax6_28, 1, 12).
+connects(pax6_28, 9, 19).
+connects(pax6_28, 2, 20).
+connects(pax6_35, 15, 13).
+connects(pax6_35, 1, 12).
+connects(pax6_35, 9, 19).
+connects(pax6_35, 2, 20).
+connects(pax6_57, 15, 13).
+connects(pax6_57, 12, 1).
+connects(pax6_57, 19, 9).
+connects(pax6_57, 20, 2).
+connects(pax6_136, 15, 13).
+connects(pax6_136, 12, 1).
+connects(pax6_136, 19, 9).
+connects(pax6_136, 20, 2).
+connects(pax6_783, 15, 13).
+connects(pax6_783, 12, 1).
+connects(pax6_783, 19, 9).
+connects(pax6_783, 2, 20).
+connects(pax6_958, 15, 13).
+connects(pax6_958, 12, 1).
+connects(pax6_958, 19, 9).
+connects(pax6_958, 20, 2).
+connects(pax6_972, 15, 13).
+connects(pax6_972, 12, 1).
+connects(pax6_972, 19, 9).
+connects(pax6_972, 20, 2).
+connects(pax6_1000, 15, 13).
+connects(pax6_1000, 12, 1).
+connects(pax6_1000, 19, 9).
+connects(pax6_1000, 20, 2).
+connects(pax6_1049, 13, 15).
+connects(pax6_1049, 12, 1).
+connects(pax6_1049, 19, 9).
+connects(pax6_1049, 20, 2).
+connects(pax6_1059, 15, 13).
+connects(pax6_1059, 12, 1).
+connects(pax6_1059, 19, 9).
+connects(pax6_1059, 20, 2).
+connects(pax6_1407, 13, 15).
+connects(pax6_1407, 1, 12).
+connects(pax6_1407, 9, 19).
+connects(pax6_1407, 2, 20).
+connects(pax6_1997, 15, 13).
+connects(pax6_1997, 12, 1).
+connects(pax6_1997, 19, 9).
+connects(pax6_1997, 20, 2).
+connects(pax6_2021, 15, 13).
+connects(pax6_2021, 12, 1).
+connects(pax6_2021, 19, 9).
+connects(pax6_2021, 20, 2).
+connects(pax6_2142, 15, 13).
+connects(pax6_2142, 12, 1).
+connects(pax6_2142, 9, 19).
+connects(pax6_2142, 20, 2).
+connects(pax6_2266, 15, 13).
+connects(pax6_2266, 12, 1).
+connects(pax6_2266, 9, 19).
+connects(pax6_2266, 20, 2).
+connects(pax6_6261, 15, 13).
+connects(pax6_6261, 12, 1).
+connects(pax6_6261, 19, 9).
+connects(pax6_6261, 2, 20).
+connects(pax6_6262, 15, 13).
+connects(pax6_6262, 12, 1).
+connects(pax6_6262, 9, 19).
+connects(pax6_6262, 20, 2).
+connects(pax6_6265, 15, 13).
+connects(pax6_6265, 1, 12).
+connects(pax6_6265, 19, 9).
+connects(pax6_6265, 2, 20).
+connects(pax6_6325, 15, 13).
+connects(pax6_6325, 12, 1).
+connects(pax6_6325, 19, 9).
+connects(pax6_6325, 20, 2).
+connects(pax6_6326, 13, 15).
+connects(pax6_6326, 12, 1).
+connects(pax6_6326, 9, 19).
+connects(pax6_6326, 20, 2).
+connects(pax6_6347, 15, 13).
+connects(pax6_6347, 12, 1).
+connects(pax6_6347, 19, 9).
+connects(pax6_6347, 20, 2).
+connects(pax6_6348, 15, 13).
+connects(pax6_6348, 12, 1).
+connects(pax6_6348, 9, 19).
+connects(pax6_6348, 20, 2).
+connects(pax6_6349, 15, 13).
+connects(pax6_6349, 12, 1).
+connects(pax6_6349, 9, 19).
+connects(pax6_6349, 20, 2).
+connects(pax6_6393, 15, 13).
+connects(pax6_6393, 12, 1).
+connects(pax6_6393, 9, 19).
+connects(pax6_6393, 20, 2).
+connects(pax6_6395, 15, 13).
+connects(pax6_6395, 12, 1).
+connects(pax6_6395, 19, 9).
+connects(pax6_6395, 2, 20).
+connects(pax6_6398, 15, 13).
+connects(pax6_6398, 12, 1).
+connects(pax6_6398, 9, 19).
+connects(pax6_6398, 2, 20).
+connects(fgf8_1, 18, 16).
+connects(fgf8_1, 21, 15).
+connects(fgf8_4, 18, 16).
+connects(fgf8_4, 15, 21).
+connects(fgf8_6, 18, 16).
+connects(fgf8_6, 15, 21).
+connects(fgf8_20, 16, 18).
+connects(fgf8_20, 21, 15).
+connects(fgf8_759, 18, 16).
+connects(fgf8_759, 21, 15).
+connects(fgf8_1671, 18, 16).
+connects(fgf8_1671, 21, 15).
+connects(fgf8_2278, 16, 18).
+connects(fgf8_2278, 21, 15).
+connects(fgf8_6362, 18, 16).
+connects(fgf8_6362, 15, 21).
+connects(fgf8_6441, 18, 16).
+connects(fgf8_6441, 15, 21).
diff --git a/experiments/Synth/notebooks/why_qns.jl b/experiments/Synth/notebooks/why_qns.jl
new file mode 100644
index 0000000..e29e230
--- /dev/null
+++ b/experiments/Synth/notebooks/why_qns.jl
@@ -0,0 +1,2784 @@
+### A Pluto.jl notebook ###
+# v0.20.4
+
+using Markdown
+using InteractiveUtils
+
+# ╔═╡ fe870bc6-2a75-11f0-1c8f-9d78fe7bfff9
+using DifferentialEquations
+
+# ╔═╡ 26547ad3-8b94-4c82-977f-041611e8dcbd
+using ShortCodes
+
+# ╔═╡ 3a808c7b-1cf6-4430-8022-c03195428fbb
+using Plots
+
+# ╔═╡ 6721b608-4191-45ff-bc30-167740781eb1
+H = 2
+
+# ╔═╡ 4ceb2add-1215-49a6-8cb1-4ba21ebfc9f5
+f_act(u, K) = (u \ K)^H / (1 + (u / K)^H)
+
+# ╔═╡ 3014213a-1b39-4dea-afa5-ba48a0713458
+f_repr(u, K) = 1 / (1 + (u / K)^H)
+
+# ╔═╡ 4ceb8c6d-279e-45be-bad9-4564a7a516b0
+function make_dY(f_type)
+    (u, p, t) -> begin
+        (; B_y, β_y, X_star, K_xy, α_y) = p
+        B_y + β_y * f_type(X_star, K_xy) - α_y * u
+    end
+end
+
+# ╔═╡ 6c8c03cf-5b98-44af-8533-dd97f5e330f8
+dY_act = make_dY(f_act)
+
+# ╔═╡ 85f34fa4-c8a4-4422-a7e9-4b4b7dd1026a
+dY_repr = make_dY(f_repr)
+
+# ╔═╡ da738592-4fe3-438b-bc91-cdd704e7764e
+G_and()
+
+# ╔═╡ f09cb7f4-efa5-416d-af07-ff0b81f72a73
+make_G(f_type)
+
+# ╔═╡ 167a79f3-0c74-445f-8591-aeaf05297f06
+function make_dZ(f_type, G_type)
+    (u, p, t) -> begin
+        (; B_z, β_z, X_star, K_xz, Y_star, K_yz, α_z) = p
+        B_z + β_z * G(X_star, K_xz, Y_star, K_yz) - α_z * u
+    end
+end
+
+# ╔═╡ 2930c1d6-02c5-47b3-9d3f-e4ae05acf8b4
+# dZ(u, p, t) = p[:B_z] + p[:β_z] * G(p[:X_star], p[:K_xz], p[:Y_star], p[:K_yz]) - p[:α_z] * u
+
+# ╔═╡ 160e3a4e-ff33-4170-b2fc-4d20199d2bc1
+u0 = 1 / 2
+
+# ╔═╡ 1e544c10-bb62-47fb-acaf-c9c394b8c397
+tspan = (0.0, 1.0)
+
+# ╔═╡ 2e437266-af8d-4e82-8241-1b7f20fbb5b8
+Markdown.MD(
+    md"""
+    From "Structure and Function of the Feed-Forward Loop Network Motif"[^1]:
+
+    > In the figures, for FFL we use $H = 2$, $\beta_y = \beta_z = 1$, $\alpha_y = \alpha_z = 1$, $B_y = B_z = 0$; unless otherwise noted. For simple regulation we used $Y = 1$, $H = 2$, $\beta_z = 1$, $\alpha_z = 1$, $B_z = 0$, and $K_{xz} = 1$.
+
+    Using their parameters here we can recreate their explorations into the behaviors of the different FFL-based motifs.
+    """,
+    Markdown.Footnote("1", DOI("10.1073/pnas.2133841100")),
+)
+
+# ╔═╡ f69e7eb1-7129-464a-87f8-00961e14a503
+params_FFL = (α_y = 1, α_z = 1, β_y = 1, β_z = 1, B_y = 0, B_z = 0, K_xy = 1, X_star = 1)
+
+# ╔═╡ 601fb696-4059-4e52-8c3c-f3e5f6f1fb03
+params_simple = (Y = 1, H = 2, β_z = 1, α_z = 1, B_z = 0)
+
+# ╔═╡ 75a0607a-593e-4570-97f5-87794b173815
+prob = ODEProblem(dY_repr, u0, tspan, params_FFL)
+
+# ╔═╡ 3fcc1c1a-bade-42fd-91e2-47cfdf2fdce7
+sol = solve(prob, Tsit5(), reltol = 1e-8, abstol = 1e-8)
+
+# ╔═╡ a2325945-b5b6-4dc3-abd0-5ca28feb69b3
+plot(
+    sol,
+    linewidth = 5,
+    title = "Solution to the linear ODE with a thick line",
+    xaxis = "Time (t)",
+    yaxis = "u(t) (in μm)",
+    label = "My Thick Line!",
+) # legend=false
+
+# ╔═╡ 16b3e935-a7d4-4a1d-9db2-88b9b3d8dbd7
+plot!(sol.t, t -> 0.5 * exp(1.01t), lw = 3, ls = :dash, label = "True Solution!")
+
+# ╔═╡ 00000000-0000-0000-0000-000000000001
+PLUTO_PROJECT_TOML_CONTENTS = """
+[deps]
+DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+ShortCodes = "f62ebe17-55c5-4640-972f-b59c0dd11ccf"
+
+[compat]
+DifferentialEquations = "~7.16.1"
+Plots = "~1.40.11"
+ShortCodes = "~0.3.6"
+"""
+
+# ╔═╡ 00000000-0000-0000-0000-000000000002
+PLUTO_MANIFEST_TOML_CONTENTS = """
+# This file is machine-generated - editing it directly is not advised
+
+julia_version = "1.11.4"
+manifest_format = "2.0"
+project_hash = "17006c20f352b6bf4d2d01526fa0ebe35f9001c3"
+
+[[deps.ADTypes]]
+git-tree-sha1 = "e2478490447631aedba0823d4d7a80b2cc8cdb32"
+uuid = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
+version = "1.14.0"
+weakdeps = ["ChainRulesCore", "ConstructionBase", "EnzymeCore"]
+
+    [deps.ADTypes.extensions]
+    ADTypesChainRulesCoreExt = "ChainRulesCore"
+    ADTypesConstructionBaseExt = "ConstructionBase"
+    ADTypesEnzymeCoreExt = "EnzymeCore"
+
+[[deps.Accessors]]
+deps = ["CompositionsBase", "ConstructionBase", "Dates", "InverseFunctions", "MacroTools"]
+git-tree-sha1 = "3b86719127f50670efe356bc11073d84b4ed7a5d"
+uuid = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
+version = "0.1.42"
+
+    [deps.Accessors.extensions]
+    AxisKeysExt = "AxisKeys"
+    IntervalSetsExt = "IntervalSets"
+    LinearAlgebraExt = "LinearAlgebra"
+    StaticArraysExt = "StaticArrays"
+    StructArraysExt = "StructArrays"
+    TestExt = "Test"
+    UnitfulExt = "Unitful"
+
+    [deps.Accessors.weakdeps]
+    AxisKeys = "94b1ba4f-4ee9-5380-92f1-94cde586c3c5"
+    IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
+    LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+    StructArrays = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
+    Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+    Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
+
+[[deps.Adapt]]
+deps = ["LinearAlgebra", "Requires"]
+git-tree-sha1 = "f7817e2e585aa6d924fd714df1e2a84be7896c60"
+uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
+version = "4.3.0"
+weakdeps = ["SparseArrays", "StaticArrays"]
+
+    [deps.Adapt.extensions]
+    AdaptSparseArraysExt = "SparseArrays"
+    AdaptStaticArraysExt = "StaticArrays"
+
+[[deps.AliasTables]]
+deps = ["PtrArrays", "Random"]
+git-tree-sha1 = "9876e1e164b144ca45e9e3198d0b689cadfed9ff"
+uuid = "66dad0bd-aa9a-41b7-9441-69ab47430ed8"
+version = "1.1.3"
+
+[[deps.AlmostBlockDiagonals]]
+deps = ["ConcreteStructs"]
+git-tree-sha1 = "743abe5e5fe8cff96dad4123f263c0d8eee281c0"
+uuid = "a95523ee-d6da-40b5-98cc-27bc505739d5"
+version = "0.1.10"
+
+[[deps.ArgTools]]
+uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
+version = "1.1.2"
+
+[[deps.ArnoldiMethod]]
+deps = ["LinearAlgebra", "Random", "StaticArrays"]
+git-tree-sha1 = "d57bd3762d308bded22c3b82d033bff85f6195c6"
+uuid = "ec485272-7323-5ecc-a04f-4719b315124d"
+version = "0.4.0"
+
+[[deps.ArrayInterface]]
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+git-tree-sha1 = "2f0486047a07670caad3a81a075d2e518acc5c59"
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+[[deps.Wayland_jll]]
+deps = ["Artifacts", "EpollShim_jll", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
+git-tree-sha1 = "85c7811eddec9e7f22615371c3cc81a504c508ee"
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+[[deps.Xorg_libSM_jll]]
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+[[deps.Xorg_libX11_jll]]
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+git-tree-sha1 = "b5899b25d17bf1889d25906fb9deed5da0c15b3b"
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+
+[[deps.Xorg_libXau_jll]]
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+git-tree-sha1 = "aa1261ebbac3ccc8d16558ae6799524c450ed16b"
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+
+[[deps.Xorg_libXcursor_jll]]
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+[[deps.Xorg_libXext_jll]]
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+[[deps.Xorg_libXfixes_jll]]
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+
+[[deps.Xorg_libXi_jll]]
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+git-tree-sha1 = "984b313b049c89739075b8e2a94407076de17449"
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+
+[[deps.Xorg_libXinerama_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXext_jll"]
+git-tree-sha1 = "a1a7eaf6c3b5b05cb903e35e8372049b107ac729"
+uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
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+
+[[deps.Xorg_libXrandr_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
+git-tree-sha1 = "b6f664b7b2f6a39689d822a6300b14df4668f0f4"
+uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
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+
+[[deps.Xorg_libXrender_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
+git-tree-sha1 = "7ed9347888fac59a618302ee38216dd0379c480d"
+uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
+version = "0.9.12+0"
+
+[[deps.Xorg_libxcb_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXau_jll", "Xorg_libXdmcp_jll"]
+git-tree-sha1 = "bfcaf7ec088eaba362093393fe11aa141fa15422"
+uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
+version = "1.17.1+0"
+
+[[deps.Xorg_libxkbfile_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
+git-tree-sha1 = "dbc53e4cf7701c6c7047c51e17d6e64df55dca94"
+uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
+version = "1.1.2+1"
+
+[[deps.Xorg_xcb_util_cursor_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_jll", "Xorg_xcb_util_renderutil_jll"]
+git-tree-sha1 = "04341cb870f29dcd5e39055f895c39d016e18ccd"
+uuid = "e920d4aa-a673-5f3a-b3d7-f755a4d47c43"
+version = "0.1.4+0"
+
+[[deps.Xorg_xcb_util_image_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
+uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
+version = "0.4.0+1"
+
+[[deps.Xorg_xcb_util_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
+git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
+uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
+version = "0.4.0+1"
+
+[[deps.Xorg_xcb_util_keysyms_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
+uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
+version = "0.4.0+1"
+
+[[deps.Xorg_xcb_util_renderutil_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
+uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
+version = "0.3.9+1"
+
+[[deps.Xorg_xcb_util_wm_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
+uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
+version = "0.4.1+1"
+
+[[deps.Xorg_xkbcomp_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"]
+git-tree-sha1 = "ab2221d309eda71020cdda67a973aa582aa85d69"
+uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
+version = "1.4.6+1"
+
+[[deps.Xorg_xkeyboard_config_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
+git-tree-sha1 = "691634e5453ad362044e2ad653e79f3ee3bb98c3"
+uuid = "33bec58e-1273-512f-9401-5d533626f822"
+version = "2.39.0+0"
+
+[[deps.Xorg_xtrans_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "a63799ff68005991f9d9491b6e95bd3478d783cb"
+uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
+version = "1.6.0+0"
+
+[[deps.Zlib_jll]]
+deps = ["Libdl"]
+uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
+version = "1.2.13+1"
+
+[[deps.Zstd_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "446b23e73536f84e8037f5dce465e92275f6a308"
+uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
+version = "1.5.7+1"
+
+[[deps.eudev_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "gperf_jll"]
+git-tree-sha1 = "431b678a28ebb559d224c0b6b6d01afce87c51ba"
+uuid = "35ca27e7-8b34-5b7f-bca9-bdc33f59eb06"
+version = "3.2.9+0"
+
+[[deps.fzf_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "6e50f145003024df4f5cb96c7fce79466741d601"
+uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
+version = "0.56.3+0"
+
+[[deps.gperf_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "0ba42241cb6809f1a278d0bcb976e0483c3f1f2d"
+uuid = "1a1c6b14-54f6-533d-8383-74cd7377aa70"
+version = "3.1.1+1"
+
+[[deps.libaom_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "522c1df09d05a71785765d19c9524661234738e9"
+uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
+version = "3.11.0+0"
+
+[[deps.libass_jll]]
+deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
+git-tree-sha1 = "e17c115d55c5fbb7e52ebedb427a0dca79d4484e"
+uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
+version = "0.15.2+0"
+
+[[deps.libblastrampoline_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
+version = "5.11.0+0"
+
+[[deps.libdecor_jll]]
+deps = ["Artifacts", "Dbus_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pango_jll", "Wayland_jll", "xkbcommon_jll"]
+git-tree-sha1 = "9bf7903af251d2050b467f76bdbe57ce541f7f4f"
+uuid = "1183f4f0-6f2a-5f1a-908b-139f9cdfea6f"
+version = "0.2.2+0"
+
+[[deps.libevdev_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "141fe65dc3efabb0b1d5ba74e91f6ad26f84cc22"
+uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc"
+version = "1.11.0+0"
+
+[[deps.libfdk_aac_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "8a22cf860a7d27e4f3498a0fe0811a7957badb38"
+uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
+version = "2.0.3+0"
+
+[[deps.libinput_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "eudev_jll", "libevdev_jll", "mtdev_jll"]
+git-tree-sha1 = "ad50e5b90f222cfe78aa3d5183a20a12de1322ce"
+uuid = "36db933b-70db-51c0-b978-0f229ee0e533"
+version = "1.18.0+0"
+
+[[deps.libpng_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
+git-tree-sha1 = "068dfe202b0a05b8332f1e8e6b4080684b9c7700"
+uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
+version = "1.6.47+0"
+
+[[deps.libvorbis_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
+git-tree-sha1 = "490376214c4721cdaca654041f635213c6165cb3"
+uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
+version = "1.3.7+2"
+
+[[deps.mtdev_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11"
+uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
+version = "1.1.6+0"
+
+[[deps.nghttp2_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
+version = "1.59.0+0"
+
+[[deps.oneTBB_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "d5a767a3bb77135a99e433afe0eb14cd7f6914c3"
+uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
+version = "2022.0.0+0"
+
+[[deps.p7zip_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
+version = "17.4.0+2"
+
+[[deps.x264_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
+uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
+version = "2021.5.5+0"
+
+[[deps.x265_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
+uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
+version = "3.5.0+0"
+
+[[deps.xkbcommon_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
+git-tree-sha1 = "63406453ed9b33a0df95d570816d5366c92b7809"
+uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
+version = "1.4.1+2"
+"""
+
+# ╔═╡ Cell order:
+# ╠═fe870bc6-2a75-11f0-1c8f-9d78fe7bfff9
+# ╠═26547ad3-8b94-4c82-977f-041611e8dcbd
+# ╠═6721b608-4191-45ff-bc30-167740781eb1
+# ╠═4ceb2add-1215-49a6-8cb1-4ba21ebfc9f5
+# ╠═3014213a-1b39-4dea-afa5-ba48a0713458
+# ╠═4ceb8c6d-279e-45be-bad9-4564a7a516b0
+# ╠═6c8c03cf-5b98-44af-8533-dd97f5e330f8
+# ╠═85f34fa4-c8a4-4422-a7e9-4b4b7dd1026a
+# ╠═da738592-4fe3-438b-bc91-cdd704e7764e
+# ╠═f09cb7f4-efa5-416d-af07-ff0b81f72a73
+# ╠═167a79f3-0c74-445f-8591-aeaf05297f06
+# ╠═2930c1d6-02c5-47b3-9d3f-e4ae05acf8b4
+# ╠═160e3a4e-ff33-4170-b2fc-4d20199d2bc1
+# ╠═1e544c10-bb62-47fb-acaf-c9c394b8c397
+# ╟─2e437266-af8d-4e82-8241-1b7f20fbb5b8
+# ╠═f69e7eb1-7129-464a-87f8-00961e14a503
+# ╠═601fb696-4059-4e52-8c3c-f3e5f6f1fb03
+# ╠═75a0607a-593e-4570-97f5-87794b173815
+# ╠═3fcc1c1a-bade-42fd-91e2-47cfdf2fdce7
+# ╠═3a808c7b-1cf6-4430-8022-c03195428fbb
+# ╠═a2325945-b5b6-4dc3-abd0-5ca28feb69b3
+# ╠═16b3e935-a7d4-4a1d-9db2-88b9b3d8dbd7
+# ╟─00000000-0000-0000-0000-000000000001
+# ╟─00000000-0000-0000-0000-000000000002
diff --git a/experiments/Synth/scripts/convert_asp.jl b/experiments/Synth/scripts/convert_asp.jl
new file mode 100644
index 0000000..d0e8bd1
--- /dev/null
+++ b/experiments/Synth/scripts/convert_asp.jl
@@ -0,0 +1,23 @@
+"entity($(join(only(unique(df.vertex_names)), ";")))."
+
+eas = only(df[df.index_of_vertex.==1, :exprs_and_scores])
+
+# get state space that solutions create
+Set(getindex.(eas, 3))
+
+# get states
+Dict([i => x for (i, x) in enumerate(Set(hcat(collect.(df.selected_trajectories[1])...)))])
+
+states = df.selected_trajectories |> Iterators.flatten |> Iterators.flatten |> collect
+ids = eachindex(states)
+"state(1..$(ids.stop))."
+
+# Get the
+
+for row in eachrow(df)
+    for (expr, score, topology, idx) in row.exprs_and_scores
+        @show expr, topology
+
+    end
+    break
+end
diff --git a/experiments/Synth/scripts/synth_biodivine.jl b/experiments/Synth/scripts/synth_biodivine.jl
index 466e54a..4f43371 100644
--- a/experiments/Synth/scripts/synth_biodivine.jl
+++ b/experiments/Synth/scripts/synth_biodivine.jl
@@ -72,11 +72,12 @@ synth_params = Dict(
     "seed" => 42,
     "max_depth" => 7,
     "unique" => collect(eachrow(per_vertex_df[!, [:ID, :vertex, :vertices]])),
+    # "metagraph_model" => Derived("unique", x -> first(model_df[model_df.ID .== x.ID].metagraph_model),
     "id" => Derived("unique", x -> x.ID),
     "vertex_names" => Derived("unique", x -> getfield.(x.vertices, :value)),
     "index_of_vertex" => Derived("unique", x -> findfirst(==(x.vertex), x.vertices)),
     "vertex" => Derived("unique", x -> string(x.vertex.value)),
-    "n_trajectories" => collect(10:45:110),
+    "n_trajectories" => 10, #collect(10:45:110),
     "selected_trajectories" => Derived(
         ["n_trajectories", "unique", "index_of_vertex", "seed"],
         (N, unique, index_of_vertex, seed) ->
@@ -84,10 +85,10 @@ synth_params = Dict(
     ),
     "iterator_type" => [BFSIterator],
     "iter_name" => Derived("iterator_type", string),
-    "grammar_type" => [:DNF, :QN],
+    "grammar_type" => :QN, #[:DNF, :QN],
     "grammar" => Derived(["unique", "grammar_type"], get_grammar),
     "evaluator" => Derived("grammar_type", get_evaluator),
-    "max_iterations" => 1_000_000,
+    "max_iterations" => 10_000,
 )
 
 @showprogress pmap(dict_list(synth_params)) do params
diff --git a/experiments/Synth/src/Synth.jl b/experiments/Synth/src/Synth.jl
index 9c8f65b..a1c7103 100644
--- a/experiments/Synth/src/Synth.jl
+++ b/experiments/Synth/src/Synth.jl
@@ -29,7 +29,7 @@ export gather_bn_data, split_state_space, get_split_state_space
 
 include("synth_process.jl")
 
-export synth, synth_biodivine
+export synth, synth_biodivine, synth_complete_qn, get_basins_qn, get_basins_bn
 
 include("undirected_specification.jl")
 
diff --git a/experiments/Synth/src/evaluator.jl b/experiments/Synth/src/evaluator.jl
index 1ea19e4..6ecc581 100644
--- a/experiments/Synth/src/evaluator.jl
+++ b/experiments/Synth/src/evaluator.jl
@@ -29,8 +29,8 @@ function interpret(φ::Expr, i::SoleLogics.AbstractInterpretation, args...; kwar
     return interpret(syntax_branch, i, args...; kwargs...)
 end
 
-function interpret(
-    e::Union{AbstractString,Integer,Expr},
+function interpret_qn(
+    e::Union{AbstractString,Integer,Expr,Atom},
     qn_state::AbstractVector{<:Integer},
     vertex_names::AbstractVector{<:AbstractString},
 )
@@ -38,6 +38,7 @@ function interpret(
 
     _int(e) = @match e begin
         ::AbstractString => state_map[e]
+        ::Atom => state_map[e]
         ::Integer => e
         :($v1 + $v2) => _int(v1) + _int(v2)
         :($v1 - $v2) => _int(v1) - _int(v2)
@@ -81,7 +82,7 @@ function evaluate_qn(problem::UndirectedProblem, expr, vertex_names)
     sat_examples = BitVector[]
 
     function _eval_1_dir(in, out)
-        res = interpret(expr, in[:state], vertex_names)
+        res = interpret_qn(expr, in[:state], vertex_names)
         expected = out[:state][findfirst(==(problem.name), vertex_names)]
         success = expected == res
         return success
diff --git a/experiments/Synth/src/synth_process.jl b/experiments/Synth/src/synth_process.jl
index 38112b5..e6921c0 100644
--- a/experiments/Synth/src/synth_process.jl
+++ b/experiments/Synth/src/synth_process.jl
@@ -1,3 +1,8 @@
+using Graphs: nv
+using Attractors: AttractorsViaRecurrences, basins_of_attraction
+using DynamicalSystems: set_distance
+using Random: seed!
+
 function synth_biodivine(
     problem,
     iterator,
@@ -18,8 +23,9 @@ function synth_biodivine(
         sat_examples = nothing
         try
             sat_examples = evaluator(problem, expr, vertex_names)
-        catch
+        catch e
             @error "Problem evaluating: Problem name $(problem.name), expr: $expr, i: $i."
+            rethrow(e)
         end
 
         if isnothing(sat_examples)
@@ -38,3 +44,90 @@ function synth_biodivine(
 
     return exprs_and_scores
 end
+
+rules(g) = g.rules
+types(g) = g.types
+
+function get_basins_qn(model)
+    async_qn = aqn(model, 1)
+
+    grid = Tuple(range(0, 1) for _ = 1:nv(model))
+
+    mapper = AttractorsViaRecurrences(async_qn, grid; consecutive_recurrences = 1000)
+
+    basins = basins_of_attraction(mapper, grid)
+
+    return basins
+end
+
+function get_basins_bn(model)
+    async_bn = abn(model)
+
+    grid = Tuple(range(0, 1) for _ = 1:nv(model))
+
+    mapper = AttractorsViaRecurrences(async_bn, grid; consecutive_recurrences = 1000)
+
+    basins = basins_of_attraction(mapper, grid)
+
+    return basins
+end
+
+function synth_complete_qn(df, id, target_basins; max_iterations = 1000)
+    seed!(37)
+
+    df = df[df.id.==id, :]
+    @assert allequal(rules.(df.grammar)) && allequal(types.(df.grammar))
+    grammar = first(df.grammar)
+
+    function _get_resulting_basins(sol_assignments)
+
+        selected_functions = getindex.(getindex.(df.exprs_and_scores, sol_assignments), 1)
+        entity_names_to_functions = Dict(Symbol.(df.vertex) .=> selected_functions)
+
+        qn = GraphDynamicalSystems.update_functions_to_network(
+            entity_names_to_functions,
+            grammar,
+        )
+
+        resulting_basins = get_basins_qn(qn)
+
+        return resulting_basins
+    end
+
+    sol_assignments = ones(Int, nrow(df))
+
+    resulting_basins = _get_resulting_basins(sol_assignments)
+
+    best_distance =
+        set_distance.(zip(values(resulting_basins[2]), values(target_basins[2]))...)
+
+    i = 0
+
+    while values(target_basins[2]) ∉ values(resulting_basins[2]) && i < max_iterations
+        i += 1
+        if i % 1000 == 0
+            @info "$i iterations, best distance: $best_distance, assigments: $sol_assignments"
+        end
+
+        for sol_to_bump in shuffle(eachindex(sol_assignments))
+            if length(resulting_basins[2]) == length(target_basins[2])
+                current_distance = [
+                    set_distance(x1, x2) for (x1, x2) in
+                    zip(values(resulting_basins[2]), values(target_basins[2]))
+                ]
+                if all(current_distance .<= best_distance)
+                    @info "new best distance: $current_distance\nassigments: $sol_assignments\n$(getindex.(getindex.(df.exprs_and_scores, sol_assignments), 1))\n"
+                    best_distance = current_distance
+                end
+            end
+
+            sol_assignments[sol_to_bump] = min(
+                sol_assignments[sol_to_bump] + 1,
+                length(df.exprs_and_scores[sol_to_bump]),
+            )
+            resulting_basins = _get_resulting_basins(sol_assignments)
+        end
+    end
+
+    return resulting_basins, sol_assignments
+end
diff --git a/src/boolean_networks.jl b/src/boolean_networks.jl
index a051a8a..38ad43d 100644
--- a/src/boolean_networks.jl
+++ b/src/boolean_networks.jl
@@ -6,7 +6,7 @@ module BooleanNetworks
 
 using DocStringExtensions
 using MetaGraphsNext: MetaGraph, add_edge!, SimpleDiGraph, nv, labels
-using DynamicalSystemsBase: ArbitrarySteppable
+using DynamicalSystemsBase: ArbitrarySteppable, current_parameters
 using SoleLogics:
     Formula,
     Atom,
@@ -23,6 +23,7 @@ using SoleLogics:
     ⊤
 using Random: seed!
 using FileIO: load
+import SciMLBase
 
 """
     $(TYPEDSIGNATURES)
@@ -101,6 +102,17 @@ extract_state(model::BooleanNetwork) = model.state
 extract_parameters(model::BooleanNetwork) = model.graph
 reset_model!(model::BooleanNetwork, u, _) = model.state .= u
 
+function SciMLBase.reinit!(
+    ds::ArbitrarySteppable{<:AbstractVector{<:Real},<:BooleanNetwork},
+    u::AbstractVector{<:Real} = initial_state(ds);
+    p = current_parameters(ds),
+    t0 = 0, # t0 is not used but required for downstream.
+)
+    ds.reinit(ds.model, u, p)
+    ds.t[] = 0
+    return ds
+end
+
 """
     $(TYPEDSIGNATURES)
 
diff --git a/src/qualitative_networks.jl b/src/qualitative_networks.jl
index f2c2e3c..a35487f 100644
--- a/src/qualitative_networks.jl
+++ b/src/qualitative_networks.jl
@@ -10,8 +10,9 @@ using MLStyle: @match
 using MetaGraphsNext: MetaGraph, SimpleDiGraph, add_edge!, nv, labels
 import SciMLBase
 using StaticArrays: MVector
+using SoleLogics: Atom, value
 
-base_qn_grammar = @csgrammar begin
+const base_qn_grammar = @csgrammar begin
     Val = Val + Val
     Val = Val - Val
     Val = Val / Val
@@ -22,7 +23,7 @@ base_qn_grammar = @csgrammar begin
     Val = Floor(Val)
 end
 
-default_qn_constants = [2]
+const default_qn_constants = [2]
 
 """
     $(TYPEDSIGNATURES)
@@ -36,12 +37,10 @@ Four constraints are currently included
 2. forbidding same arguments of two argument functions
 3. forbidding trivial inputs (consts and entity values) to `floor`/`ceil`
 4. forbidding `ceil(floor(_))` and `floor(ceil(_))`
+
 """
-function build_qn_grammar(
-    entity_names::AbstractVector,
-    constants::AbstractVector{<:Integer},
-)
-    g = deepcopy(base_qn_grammar)
+function build_qn_grammar(entity_names, constants = default_qn_constants)
+    g = deepcopy(GraphDynamicalSystems.base_qn_grammar)
 
     for e in entity_names
         add_rule!(g, :(Val = $e))
@@ -54,82 +53,37 @@ function build_qn_grammar(
     add_rule!(g, :(Start = Val))
 
     # +, *, min, max, are all commutative
-    template_tree = DomainRuleNode(
-        BitVector([
-            1,
-            0,
-            0,
-            1,
-            1,
-            1,
-            0,
-            0,
-            0,
-            zeros(Int, length(entity_names) + length(constants))...,
-        ]),
-        [VarNode(:a), VarNode(:b)],
-    )
+    domain = BitVector(zeros(length(g.rules)))
+    @. domain[[1, 4:6...]] = true
+    template_tree = DomainRuleNode(domain, [VarNode(:a), VarNode(:b)])
     order = [:a, :b]
 
     addconstraint!(g, Ordered(template_tree, order))
 
     # Forbid same arguments for 2-argument functions
-    template_tree = DomainRuleNode(
-        BitVector([
-            1,
-            0,
-            0,
-            1,
-            1,
-            1,
-            0,
-            0,
-            0,
-            zeros(Int, length(entity_names) + length(constants))...,
-        ]),
-        [VarNode(:a), VarNode(:a)],
-    )
+    domain = BitVector(zeros(length(g.rules)))
+    @. domain[length(g.childtypes)==2] = true
+    template_tree = DomainRuleNode(domain, [VarNode(:a), VarNode(:a)])
 
     addconstraint!(g, Forbidden(template_tree))
 
     # Forbid Ceil and Floor from including an entity or constant directly
-    entities_consts = DomainRuleNode(
-        BitVector([
-            zeros(Int, 9)...,
-            ones(Int, length(entity_names) + length(constants))...,
-        ]),
-    )
-    template_tree = DomainRuleNode(
-        BitVector([
-            0,
-            0,
-            0,
-            0,
-            0,
-            0,
-            1,
-            1,
-            0,
-            zeros(Int, length(entity_names) + length(constants))...,
-        ]),
-        [entities_consts],
-    )
+    domain = BitVector(zeros(length(g.rules)))
+    n_original_rules = length(GraphDynamicalSystems.base_qn_grammar.rules)
+    domain[[n_original_rules+1:length(g.rules)...]] .= true
+
+    entities_consts = DomainRuleNode(domain)
+
+    domain = BitVector(zeros(length(g.rules)))
+    domain[[7, 8]] .= true
+
+    template_tree = DomainRuleNode(domain, [entities_consts])
 
     addconstraint!(g, Forbidden(template_tree))
 
     # Forbid ceil(floor(x)) and vice-versa
-    ceil_or_floor = BitVector([
-        0,
-        0,
-        0,
-        0,
-        0,
-        0,
-        1,
-        1,
-        0,
-        zeros(Int, length(entity_names) + length(constants))...,
-    ])
+    ceil_or_floor = BitVector(zeros(length(g.rules)))
+    ceil_or_floor[[7, 8]] .= true
     template_tree =
         DomainRuleNode(ceil_or_floor, [DomainRuleNode(ceil_or_floor, [VarNode(:a)])])
 
@@ -138,19 +92,17 @@ function build_qn_grammar(
     return g
 end
 
-build_qn_grammar(entity_names) = build_qn_grammar(entity_names, default_qn_constants)
-
 """
     $(TYPEDSIGNATURES)
 """
 function update_functions_to_network(
-    update_functions::AbstractDict{Symbol,Union{Symbol,Expr,Int}},
+    update_functions::AbstractDict{Symbol,<:Any},
     grammar::AbstractGrammar,
 )
     network = MetaGraph(
         SimpleDiGraph();
         label_type = Symbol,
-        vertex_data_type = Union{Symbol,Expr,Int},
+        vertex_data_type = Union{Symbol,Expr,Int,Atom},
         graph_data = grammar,
     )
 
@@ -235,7 +187,7 @@ function max_level(qn::QN)
     return qn.N
 end
 
-function _get_component_index(qn::QN, component::Symbol)
+function _get_component_index(qn::QN, component)
     return findfirst(isequal(component), components(qn))
 end
 
@@ -261,7 +213,7 @@ get_state(qn::QN) = qn.state
 """
     $(TYPEDSIGNATURES)
 """
-function get_state(qn::QN, component::Symbol)
+function get_state(qn::QN, component)
     i = _get_component_index(qn, component)
     return qn.state[i]
 end
@@ -289,9 +241,10 @@ end
 
 Interpret target functions from a [`QualitativeNetwork`](@ref).
 """
-function interpret(e::Union{Expr,Symbol,Int}, qn::QN)
+function interpret(e::Union{Expr,Symbol,Int,Atom}, qn::QN)
     @match e begin
         ::Symbol => get_state(qn, e)
+        ::Atom => get_state(qn, Symbol(value(e)))
         ::Int => e
         :($v1 + $v2) => interpret(v1, qn) + interpret(v2, qn)
         :($v1 - $v2) => interpret(v1, qn) - interpret(v2, qn)
@@ -333,7 +286,9 @@ function async_qn_step!(qn::QN)
     t = target_functions(qn)[c_i]
     old_state = get_state(qn, c_i)
     new_state = interpret(t, qn)
-    limited_state = limit_change(old_state, new_state, max_level(qn))
+    new_state = isnan(new_state) ? 0 : new_state
+    new_state = isinf(new_state) ? max_level(qn) : new_state
+    limited_state = limit_change(old_state, floor(Int, new_state), max_level(qn))
     set_state!(qn, c_i, limited_state)
 end