index.json

[{"authors":null,"categories":null,"content":"","date":-62135596800,"expirydate":-62135596800,"kind":"term","lang":"en","lastmod":-62135596800,"objectID":"49330e8e0b51e25fe58a56e7557b5ccd","permalink":"","publishdate":"0001-01-01T00:00:00Z","relpermalink":"","section":"authors","summary":"","tags":null,"title":"Luis Benet","type":"authors"},{"authors":null,"categories":null,"content":"Born in Uruguay (Montevideo, 1988), I graduated in Physics from Univ. de la República (Facultad de Ciencias), and in Electrical Engineering (Facultad de Ingeniería). I moved to France for a PhD in Mathematics and Informatics (Univ. Joseph Fourier, 2013-2015), writing a thesis on the quantum random walk, a mathematical model of particular interest in Quantum Computing.\nI\u0026rsquo;m a former post-doc researcher at VERIMAG laboratory of Université Grenoble Alpes (2016-2017), a leading French research center in embedded systems that are used in diverse disciplines such as avionics/aeronautics, space, transport, automotive, telecommunications, smart cards and consumer electronics. As an Applied Mathematician, my research has to do with developing innovative numerical tools that impact decisions regarding reliability, correctness and safety of systems. I specialize on formal verification of Cyber-Physical Systems (CPS), hybrid dynamical systems, and robustness analysis of neural networks.\nIf you are interested to discuss, get in touch! You can email me to mforets at gmail.com.\n","date":1612546162,"expirydate":-62135596800,"kind":"term","lang":"en","lastmod":1612546162,"objectID":"2525497d367e79493fd32b198b28f040","permalink":"","publishdate":"0001-01-01T00:00:00Z","relpermalink":"","section":"authors","summary":"Born in Uruguay (Montevideo, 1988), I graduated in Physics from Univ. de la República (Facultad de Ciencias), and in Electrical Engineering (Facultad de Ingeniería). I moved to France for a PhD in Mathematics and Informatics (Univ.","tags":null,"title":"Marcelo Forets","type":"authors"},{"authors":null,"categories":null,"content":"","date":-62135596800,"expirydate":-62135596800,"kind":"term","lang":"en","lastmod":-62135596800,"objectID":"d4c9823dac39d787428220d0fd3222b2","permalink":"","publishdate":"0001-01-01T00:00:00Z","relpermalink":"","section":"authors","summary":"","tags":null,"title":"Daniel Freire Caporale","type":"authors"},{"authors":null,"categories":null,"content":"","date":-62135596800,"expirydate":-62135596800,"kind":"term","lang":"en","lastmod":-62135596800,"objectID":"2f0a565792c3cdcb13b95e7ca111f701","permalink":"","publishdate":"0001-01-01T00:00:00Z","relpermalink":"","section":"authors","summary":"","tags":null,"title":"Sebastian Guadalupe","type":"authors"},{"authors":null,"categories":null,"content":"","date":-62135596800,"expirydate":-62135596800,"kind":"term","lang":"en","lastmod":-62135596800,"objectID":"786dad0cf29275258ed2c9f6992490a9","permalink":"","publishdate":"0001-01-01T00:00:00Z","relpermalink":"","section":"authors","summary":"","tags":null,"title":"Jorge Pérez Zerpa","type":"authors"},{"authors":null,"categories":null,"content":"","date":-62135596800,"expirydate":-62135596800,"kind":"term","lang":"en","lastmod":-62135596800,"objectID":"de191098a4a009447b88b4c020d51658","permalink":"","publishdate":"0001-01-01T00:00:00Z","relpermalink":"","section":"authors","summary":"","tags":null,"title":"David P. Sanders","type":"authors"},{"authors":null,"categories":null,"content":"Christian Schilling is a computer scientist interested in analysis, formal verification, and synthesis of dynamical, cyber-physical, and software systems, and explainable artificial intelligence. Currently working at the University of Konstanz, Germany, received his Ph.D. degree under supervision of Andreas Podelski from the University of Freiburg, Germany, in 2018. Former postdoctoral fellow with Thomas A. Henzinger at IST Austria.\n","date":-62135596800,"expirydate":-62135596800,"kind":"term","lang":"en","lastmod":-62135596800,"objectID":"9e56f752d974ea87219b284ef6178229","permalink":"","publishdate":"0001-01-01T00:00:00Z","relpermalink":"","section":"authors","summary":"Christian Schilling is a computer scientist interested in analysis, formal verification, and synthesis of dynamical, cyber-physical, and software systems, and explainable artificial intelligence. Currently working at the University of Konstanz, Germany, received his Ph.","tags":null,"title":"Christian Schilling","type":"authors"},{"authors":[],"categories":null,"content":" Click on the Slides button above to view the built-in slides feature.   Slides can be added in a few ways:\n Create slides using Wowchemy\u0026rsquo;s Slides feature and link using slides parameter in the front matter of the talk file Upload an existing slide deck to static/ and link using url_slides parameter in the front matter of the talk file Embed your slides (e.g. Google Slides) or presentation video on this page using shortcodes.  Further event details, including page elements such as image galleries, can be added to the body of this page.\n","date":1906549200,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1906549200,"objectID":"a8edef490afe42206247b6ac05657af0","permalink":"https://juliareach.github.io/talk/example-talk/","publishdate":"2017-01-01T00:00:00Z","relpermalink":"/talk/example-talk/","section":"event","summary":"An example talk using Wowchemy's Markdown slides feature.","tags":[],"title":"Example Talk","type":"event"},{"authors":["Marcelo Forets"],"categories":[],"content":"\u0026laquo; WORK-IN-PROGRESS\u0026raquo;\nContext Let an initial-value problem be specified as follows:\n$$ y'(t) = f(t, y),\\qquad y(t_0) = y_0.\\qquad (1) $$ Here $y \\in \\mathbb{R}^m$ is an unknown function of time $t$.\nWe will consider a naive Julia implementation of the famous fourth-order explicit Runge-Kutta integration method. The idea is to use such method to solve (1) for the case when $y_0$ is defined symbolically in the sense that we replace $y_0$ by $y_0 + \\xi$ where $\\xi$ is a vector of $m$ \u0026ldquo;symbols\u0026rdquo;. We would like to evaluate how does the classic RK4 method propagate the $\\xi$ and see what information can be extracted from such expansion.\nIn this method, given a step size $h \u0026gt; 0$ we compute for each $n = 0, 1, 2, \\ldots, N$ a sequence $y_1, y_2, \\ldots, y_N$ using an explicit scheme of the form $y_{n+1} = y_n + h \\sum_{i=1}^s b_i k_i$, where the $k_i$ are obtained by evaluating $f(t, y)$ on intermediate points. In the case of RK4 one step of the algorithm is obtained with the following step function.\nfunction step!(f, y, n, t, h) k₁ = f(t[n], y[n]) k₂ = f(t[n] + h/2, y[n] + h*k₁/2) k₃ = f(t[n] + h/2, y[n] + h*k₂/2) k₄ = f(t[n] + h, y[n] + h*k₃) y[n+1] = y[n] + (h/6) * (k₁ + 2k₂ + 2k₃ + k₄) t[n+1] = t[n] + h end  step! (generic function with 1 method)  function solve(f, h, t₀, T, y₀) N = round(Int, (T - t₀) / h) t = Vector{Float64}(undef, N) y = Vector{typeof(y₀)}(undef, N) y[1] = y₀; t[1] = t₀; for n in 1:N-1 step!(f, y, n, t, h) end y, t end  solve (generic function with 1 method)  Example Consider the quadratic ODE\n$$ y'(t) = 1 - y^2,\\qquad y(t_0) = 0,~~ t \\in [0, 10]. $$\nWe consider a step size $h = 0.01$.\nf_quad(t, y) = 1 - y^2  f_quad (generic function with 1 method)  r, t = solve(f_quad, 0.01, 0.0, 10.0, 0.0);  using Plots  plot(t, r, seriestype=:line, lab=\u0026quot;\u0026quot;, xlab=\u0026quot;t\u0026quot;, ylab=\u0026quot;y(t)\u0026quot;)  Now suppose that we solve the recurrence with an initial state $u_0 + \\xi$.\nusing TaylorSeries  ξ = Taylor1(20) set_taylor1_varname(\u0026quot;ξ\u0026quot;) u0 = 0.0 u0ξ = u0 + ξ   1.0 ξ + 𝒪(ξ²¹)  y, t = solve(f_quad, 0.01, 0.0, 10.0, u0ξ); length(y)  1000  y[1]   1.0 ξ + 𝒪(ξ²¹)  y[2]   0.009999666679166094 + 0.99990000666625 ξ - 0.009998666787493126 ξ² + 9.998333499990624e-5 ξ³ - 9.997958521864687e-7 ξ⁴ + 9.997916857282813e-9 ξ⁵ - 9.581395992702446e-11 ξ⁶ + 8.331729276038803e-13 ξ⁷ - 6.821796933983367e-15 ξ⁸ + 4.8430989824216484e-17 ξ⁹ - 2.968450528059874e-19 ξ¹⁰ + 1.5103098972005213e-21 ξ¹¹ - 6.119511719889326e-24 ξ¹² + 1.9530794270833342e-26 ξ¹³ - 4.557259114583335e-29 ξ¹⁴ + 6.510416666666671e-32 ξ¹⁵ - 4.069010416666671e-35 ξ¹⁶ + 𝒪(ξ²¹)  y[3]   0.019997333758263312 + 0.9996001066422828 ξ - 0.019989336973987328 ξ² + 0.0003997334431869484 ξ³ - 7.993594720222507e-6 ξ⁴ + 1.5985124640472037e-7 ξ⁵ - 3.1883090638671063e-9 ξ⁶ + 6.325950825886493e-11 ξ⁷ - 1.2462287616432512e-12 ξ⁸ + 2.4312653056785857e-14 ξ⁹ - 4.687998642014969e-16 ξ¹⁰ + 8.919632391826903e-18 ξ¹¹ - 1.672458814319322e-19 ξ¹² + 3.08748726849809e-21 ξ¹³ - 5.608112595223544e-23 ξ¹⁴ + 1.0018858671317283e-24 ξ¹⁵ - 1.7600522287738262e-26 ξ¹⁶ + 3.040358425374431e-28 ξ¹⁷ - 5.164849498520435e-30 ξ¹⁸ + 8.629961159714198e-32 ξ¹⁹ - 1.4187146313423383e-33 ξ²⁰ + 𝒪(ξ²¹)  y[4]   0.029991003236316215 + 0.9991005397242128 ξ - 0.02996402754525644 ξ² + 0.000898651247751589 ξ³ - 2.6951439926918567e-5 ξ⁴ + 8.083018387635607e-7 ξ⁵ - 2.4229420975103902e-8 ξ⁶ + 7.255492265663734e-10 ξ⁷ - 2.169261345744115e-11 ξ⁸ + 6.471370059589956e-13 ξ⁹ - 1.9250541717144024e-14 ξ¹⁰ + 5.706694617811968e-16 ξ¹¹ - 1.6849037837381005e-17 ξ¹² + 4.952171150219145e-19 ξ¹³ - 1.4482976068740724e-20 ξ¹⁴ + 4.213120613390775e-22 ξ¹⁵ - 1.2187249982451306e-23 ξ¹⁶ + 3.504794249260267e-25 ξ¹⁷ - 1.0018397840714965e-26 ξ¹⁸ + 2.846156443714574e-28 ξ¹⁹ - 8.035424335081523e-30 ξ²⁰ + 𝒪(ξ²¹)  y[5]   0.03997868030782012 + 0.9984017051196238 ξ - 0.03991478262103181 ξ² + 0.0015957403355221493 ξ³ - 6.379557597746384e-5 ξ⁴ + 2.550464580022681e-6 ξ⁵ - 1.0194784965344293e-7 ξ⁶ + 4.073770468253297e-9 ξ⁷ - 1.6270188569216327e-10 ξ⁸ + 6.4933229278608814e-12 ξ⁹ - 2.588889266950159e-13 ξ¹⁰ + 1.0309124077397989e-14 ξ¹¹ - 4.099036112193993e-16 ξ¹² + 1.6269963041530542e-17 ξ¹³ - 6.445181115936467e-19 ξ¹⁴ + 2.5476149615176444e-20 ξ¹⁵ - 1.0046100402336236e-21 ξ¹⁶ + 3.9513947849926016e-23 ξ¹⁷ - 1.549979598640151e-24 ξ¹⁸ + 6.062710831558582e-26 ξ¹⁹ - 2.3644194573304648e-27 ξ²⁰ + 𝒪(ξ²¹)  The result is a sequence of polynomials in $\\xi$. However such characterization is only useful for small deviations with respect to the initial state \u0026ndash; and we haven\u0026rsquo;t yet characterized the error of the approximation. For example, suppose that we are interested in $y(t = 1)$:\nt[100]  0.9900000000000007  y[100]   0.7573623240820949 + 0.4264023097949346 ξ - 0.3229410443236415 ξ² + 0.24458338018660747 ξ³ - 0.1852382373895675 ξ⁴ + 0.14029246208258747 ξ⁵ - 0.10625222517422822 ξ⁶ + 0.08047143220209468 ξ⁷ - 0.06094603090212832 ξ⁸ + 0.046158227586616425 ξ⁹ - 0.03495850249638864 ξ¹⁰ + 0.026476252672553414 ξ¹¹ - 0.02005211623341677 ξ¹² + 0.015186717331102878 ξ¹³ - 0.01150184751249755 ξ¹⁴ + 0.008711065944387024 ξ¹⁵ - 0.006597433131544507 ξ¹⁶ + 0.004996647273657277 ξ¹⁷ - 0.003784272377387678 ξ¹⁸ + 0.0028660653096264452 ξ¹⁹ - 0.0021706498720577556 ξ²⁰ + 𝒪(ξ²¹)  We can evaluate this result at $\\xi = 0$:\nevaluate(y[100], 0.0)  0.7573623240820949  At a value $\\xi = 0.1$\nevaluate(y[100], 0.1)  0.7970005083277867  And also an interval:\nusing IntervalArithmetic evaluate(y[100], -0.1 .. 0.1)  [0.711228, 0.800249]  Flowpipe using ReachabilityAnalysis const RA = ReachabilityAnalysis  ReachabilityAnalysis  @taylorize function _f_quad(du, u, p, t) du[1] = 1 - u[1]^2 end prob = @ivp(x' = _f_quad(x), dim=1, x(0) ∈ -0.1 .. 0.1); sol = RA.solve(prob, tspan=(0.0, 10.0), alg=TMJets(abs_tol=1e-12));  plot(sol, vars=(0, 1), alpha=.2) plot!(t, r, seriestype=:line, lab=\u0026quot;\u0026quot;)  R = sol(1.0)  TaylorModelReachSet{Float64}(TaylorModels.TaylorModel1{TaylorN{Float64},Float64}[ 0.7549628871907649 + 0.043003103896458415 x₁ - 0.0032465747475834863 x₁² + ( 0.4300310389645844 - 0.06493149495166935 x₁ + 0.003052819945102918 x₁²) ξ + ( - 0.32465747475834694 + 0.03052819945102888 x₁ + 0.0018836179755100605 x₁²) ξ² + ( 0.101760664836763 + 0.012557453170067179 x₁ - 0.00480650040545221 x₁²) ξ³ + ( 0.03139363292516797 - 0.024032502027261038 x₁ + 0.0027912209062894602 x₁²) ξ⁴ + ( - 0.048065004054522104 + 0.011164883625157804 x₁ + 0.0006981330083023078 x₁²) ξ⁵ + ( 0.018608139375263018 + 0.0023271100276743783 x₁ - 0.0020517845820511183 x₁²) ξ⁶ + ( 0.0033244428966776847 - 0.005862241663003196 x₁ + 0.001163377855574074 x₁²) ξ⁷ + ( - 0.007327802078754001 + 0.0029084446389351804 x₁ + 0.0001265493671184609 x₁²) ξ⁸ + [-3.86101e-14, 3.14375e-14]], [0.984396, 1.02463])  tspan(R)  [0.984396, 1.02463]  Z = polynomial.(set(R))  1-element Array{Taylor1{TaylorN{Float64}},1}: 0.7549628871907649 + 0.043003103896458415 x₁ - 0.0032465747475834863 x₁² + 𝒪(‖x‖³) + ( 0.4300310389645844 - 0.06493149495166935 x₁ + 0.003052819945102918 x₁² + 𝒪(‖x‖³)) ξ + ( - 0.32465747475834694 + 0.03052819945102888 x₁ + 0.0018836179755100605 x₁² + 𝒪(‖x‖³)) ξ² + ( 0.101760664836763 + 0.012557453170067179 x₁ - 0.00480650040545221 x₁² + 𝒪(‖x‖³)) ξ³ + ( 0.03139363292516797 - 0.024032502027261038 x₁ + 0.0027912209062894602 x₁² + 𝒪(‖x‖³)) ξ⁴ + ( - 0.048065004054522104 + 0.011164883625157804 x₁ + 0.0006981330083023078 x₁² + 𝒪(‖x‖³)) ξ⁵ + ( 0.018608139375263018 + 0.0023271100276743783 x₁ - 0.0020517845820511183 x₁² + 𝒪(‖x‖³)) ξ⁶ + ( 0.0033244428966776847 - 0.005862241663003196 x₁ + 0.001163377855574074 x₁² + 𝒪(‖x‖³)) ξ⁷ + ( - 0.007327802078754001 + 0.0029084446389351804 x₁ + 0.0001265493671184609 x₁² + 𝒪(‖x‖³)) ξ⁸ + 𝒪(ξ⁹)  using LazySets using LazySets: Interval  out = [Singleton([ti]) × Interval(evaluate(yi, -0.1 .. 0.1)) for (ti, yi) in zip(t, y)];  plot(out, marker=:x)  plot!(sol, vars=(0, 1), alpha=.2)  plot(sol[1:30], vars=(0, 1), alpha=.2, c=:lightblue) plot!(out[1:100], marker=:x, c=:red)  ","date":1612546162,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1612546162,"objectID":"5c2133a1cdc2fd27a97bc3ffa27f407b","permalink":"https://juliareach.github.io/post/rk4_taylorseries/","publishdate":"2021-02-05T14:29:22-03:00","relpermalink":"/post/rk4_taylorseries/","section":"post","summary":" ","tags":["Reachability"],"title":"Taylor expanding ODE solutions","type":"post"},{"authors":null,"categories":null,"content":"","date":1612137600,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1612137600,"objectID":"959439f4ae8b854f99fb6b908943d1e5","permalink":"https://juliareach.github.io/software/reachabilityanalysis/","publishdate":"2021-02-01T00:00:00Z","relpermalink":"/software/reachabilityanalysis/","section":"software","summary":"Methods to compute sets of states reachable by dynamical systems","tags":null,"title":"ReachabilityAnalysis.jl","type":"software"},{"authors":null,"categories":null,"content":"","date":1611705600,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1611705600,"objectID":"8b6a24b92a56d8dfa76fec77371c89b4","permalink":"https://juliareach.github.io/software/lazysets/","publishdate":"2021-01-27T00:00:00Z","relpermalink":"/software/lazysets/","section":"software","summary":"A Julia package for calculus with convex sets","tags":null,"title":"LazySets.jl","type":"software"},{"authors":["Marcelo Forets"],"categories":null,"content":"Prize announcement The ARCH 2020 Best Result Award goes to Luis Benet, Marcelo Forets, Daniel Freire, David P. Sanders, and Christian Schilling (in alphabetical order) for their verification tool JuliaReach. The award comes with a 500 Euro prize. Congratulations!\nResolution We will give the prize to Sebastian (@sebastianguadalupe), a Uruguayan undergraduate student who collabored with us on the Julia Seasons of Contributions 2020 edition.\nSebastian will work on zonotope-based methods applied to hybrid systems. He will be writing a tool for reachability analysis of neural-network controlled systems to leverage on the JuliaReach ecosystem and sisl/NeuralVerification.jl from the Stanford Intelligent Systems Laboratory library.\n","date":1607817600,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1607817600,"objectID":"7851aa2db397f86c99bfd4edb002cde9","permalink":"https://juliareach.github.io/post/archcomp20_prize/","publishdate":"2020-12-13T00:00:00Z","relpermalink":"/post/archcomp20_prize/","section":"post","summary":" ","tags":["ARCH-COMP"],"title":"Best Result Award: Applied Verification for Continuous and Hybrid Systems 2020","type":"post"},{"authors":null,"categories":null,"content":"Publication Abstract Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous and discrete post operators to compute states reachable according to continuous and discrete dynamics, respectively. In this article, we enhance both of these operators and make sure that most of the involved computations are performed in low-dimensional state space. In particular, we improve the continuous-post operator by performing computations in high-dimensional state space only for time intervals relevant for the subsequent application of the discrete-post operator. Furthermore, the new discrete-post operator performs low-dimensional computations by leveraging the structure of the guard and assignment of a considered transition. We illustrate the potential of our approach on a number of challenging benchmarks.\nContributions Presentation   Presentation slides (pdf) are available here.\n  The recording for EMSOFT'20 is available here.\n  How to cite @article{forets2020efficient, title={Efficient reachability analysis of parametric linear hybrid systems with time-triggered transitions}, author={Forets, Marcelo and Freire, Daniel and Schilling, Christian}, journal={arXiv preprint arXiv:2006.12325}, year={2020} }  ","date":1604188800,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1604188800,"objectID":"8ae7a4f32d454b5a57bd5501cb143a6e","permalink":"https://juliareach.github.io/project/decohybrid/","publishdate":"2020-11-01T00:00:00Z","relpermalink":"/project/decohybrid/","section":"project","summary":"by Sergiy Bogomolov, Marcelo Forets, Goran Frehse, Kostiantyn Potomkin, Christian Schilling (2020)","tags":["Reachability","Hybrid systems","Decomposition"],"title":"Reachability analysis of linear hybrid systems via block decomposition","type":"project"},{"authors":null,"categories":null,"content":"Publication Case Study: Reachability Analysis of a unified Combat-Command-and-Control Model. Sergiy Bogomolov, Marcelo Forets, Kostiantyn Potomkin. International Conference on Reachability Problems (2020). Lecture Notes in Computer Science, vol 12448. (2020) doi: 10.1007/978-3-030-61739-4_4.\nPresented in the 14th International Conference on Reachability Problems 2020.\nAbstract Reachability analysis computes an envelope encompassing the reachable states of a hybrid automaton within a given time horizon. It is known to be a computationally intensive task. In this case study paper, we consider the application of reachability analysis on a mathematical model unifying two key warfighting functions: Combat, and Commandand-Control (C2). Reachability here has a meaning of whether, given a range of initial combat forces and a C2 network and various uncertainties, one side can survive combat with intact forces while the adversary is diminished to zero. These are questions which arise in military Operations Research (OR). This paper is the first to utilize the notions of a hybrid automaton and reachability analysis in the area of OR. We explore the applicability and scalability of Taylor-model based reachability techniques in this domain. Our experiments demonstrate the potential of reachability analysis in the context of OR.\nContributions We have explored the feasibility of applying some state-of-the-art reachability tools on a mathematical model unifying the dynamics of combat and C2. Operations Research is a domain where the advantages of using reachability analysis are yet to be discovered, and our contribution is a first step towards that direction. The unified combat model considered appears to be a challenging case study model, and although current verification techniques demonstrate capabilities to verify the systems up to the necessary time horizon of the model, there are still relevant configurations where reachability tools fail to verify the system. In particular, we investigated the method based on Taylor models in Flow* and JuliaReach for cases where the C2 takes place on networks of size N = 3, 5 and 10. Given a certain uncertainty on initial conditions for Blue and Red combat forces we were able to derive reach-tubes for the subsequent time-evolution, bounding the behaviours of both forces and determining whether one side or the other is guaranteed success in the combat outcome.\nIn conclusion, the approach with adaptive time step (JuliaReach) has shown the best scalability. We emphasise that here we examined reachability within the constraint that the reach-tubes should cover all possible behaviors of the system’s evolution. However, we anticipate that significant scaling benefits may be achieved by relaxing this condition, thus testing that certain states may be reached while allowing for a degree of approximation.\nHow to cite @inproceedings{bogomolov2020case, title={Case Study: Reachability and Scalability in a Unified Combat-Command-and-Control Model}, author={Bogomolov, Sergiy and Forets, Marcelo and Potomkin, Kostiantyn}, booktitle={International Conference on Reachability Problems}, pages={52--66}, year={2020}, organization={Springer} }  ","date":1602720000,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1602720000,"objectID":"c2884537d70ea6ef3fe96252b0b729d9","permalink":"https://juliareach.github.io/project/ccc/","publishdate":"2020-10-15T00:00:00Z","relpermalink":"/project/ccc/","section":"project","summary":"by Sergiy Bogomolov, Marcelo Forets, Kostiantyn Potomkin (2020)","tags":["Hybrid automata","Reachability analysis","Operations research"],"title":"Case Study: Reachability and Scalability in a Unified Combat-Command-and-Control Model","type":"project"},{"authors":null,"categories":null,"content":"Publication ARCH-COMP19 Category Report: Continuous and Hybrid Systems with Linear Continuous Dynamics. Matthias Althoff, Stanley Bak, Marcelo Forets, Goran Frehse, Niklas Kochdumper, Rajarshi Ray, Christian Schilling and Stefan Schupp (2019) ARCH19. 6th International Workshop on Applied Verification of Continuous and Hybrid Systems, vol 61, pages 14\u0026ndash;40 doi: 10.29007/bj1w.\nAbstract Contributions How to cite   ","date":1600992000,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1600992000,"objectID":"c4350733516c4a0565d188dfc8418d3e","permalink":"https://juliareach.github.io/project/archcomp19_aff/","publishdate":"2020-09-25T00:00:00Z","relpermalink":"/project/archcomp19_aff/","section":"project","summary":"by Matthias Althoff, Stanley Bak, Marcelo Forets, Goran Frehse, Niklas Kochdumper, Rajarshi Ray, Christian Schilling and Stefan Schupp","tags":["Reachability","ARCH-COMP"],"title":"ARCH-COMP19 Category Report: Continuous and Hybrid Systems with Linear Continuous Dynamics","type":"project"},{"authors":null,"categories":null,"content":"Publication ARCH-COMP20 Category Report: Continuous and Hybrid Systems with Linear Continuous Dynamics. Matthias Althoff, Stanley Bak, Zongnan Bao, Marcelo Forets, Daniel Freire, Goran Frehse, Niklas Kochdumper, Yangge Li, Sayan Mitra, Rajarshi Ray, Christian Schilling, Stefan Schupp, and Mark Wetzlinger (2020) ARCH20. 7th International Workshop on Applied Verification of Continuous and Hybrid Systems. 7th International Workshop on Applied Verification of Continuous and Hybrid Systems (ARCH20), vol 74, pages 16\u0026ndash;48. 10.29007/7dt2.\nAbstract We present the results of the ARCH 2020 (Workshop on Applied Verification for Continuous and Hybrid Systems friendly competition for formal verification of continuous and hybrid systems with linear continuous dynamics. In its fourth edition, eight tools have been applied to solve eight different benchmark problems in the category for linear continuous dynamics (in alphabetical order): CORA, C2E2, HyDRA, Hylaa, Hylaa-Continuous, JuliaReach, SpaceEx, and XSpeed. This report is a snapshot of the current landscape of tools and the types of benchmarks they are particularly suited for. Due to the diversity of problems, we are not ranking tools, yet the presented results provide one of the most complete assessments of tools for the safety verification of continuous and hybrid systems with linear continuous dynamics up to this date.\nContributions We consider the verification of hybrid systems (i.e., mixed discrete/continuous systems) with linear continuous dynamics $$ \\dot{x}(t) = Ax(t) + Bu(t), $$ where $A \\in \\mathbb{R}^{n \\times n}$, $x \\in \\mathbb{R}^n$, $B \\in \\mathbb{R}^{n \\times m}$, and $u \\in \\mathbb{R}^m$. For all results reported by each participant, we have run an independent repeatability evaluation. To establish further trustworthiness of the results, the code with which the results have been obtained is publicly available here. The selection of the benchmarks has been conducted within the forum of the ARCH website (here), which is visible for registered users and registration is open to anybody. All tools presented in this report use some form of reachability analysis. This, however, is not a constraint set by the organizers of the friendly competition. We hope to encourage further tool developers to showcase their results in future editions.\nHow to cite @inproceedings{ARCH20:ARCH_COMP20_Category_Report_Continuous, author = {Matthias Althoff and Stanley Bak and Zongnan Bao and Marcelo Forets and Goran Frehse and Daniel Freire and Niklas Kochdumper and Yangge Li and Sayan Mitra and Rajarshi Ray and Christian Schilling and Stefan Schupp and Mark Wetzlinger}, title = {ARCH-COMP20 Category Report: Continuous and Hybrid Systems with Linear Continuous Dynamics}, booktitle = {ARCH20. 7th International Workshop on Applied Verification of Continuous and Hybrid Systems (ARCH20)}, editor = {Goran Frehse and Matthias Althoff}, series = {EPiC Series in Computing}, volume = {74}, pages = {16--48}, year = {2020}, publisher = {EasyChair}, bibsource = {EasyChair, https://easychair.org}, issn = {2398-7340}, url = {https://easychair.org/publications/paper/DRpS}, doi = {10.29007/7dt2} }  ","date":1600992000,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1600992000,"objectID":"d6cad04a8d05a81979f526eaeb6216a1","permalink":"https://juliareach.github.io/project/archcomp20_aff/","publishdate":"2020-09-25T00:00:00Z","relpermalink":"/project/archcomp20_aff/","section":"project","summary":"by Matthias Althoff, Stanley Bak, Zongnan Bao, Marcelo Forets, Daniel Freire, Goran Frehse, Niklas Kochdumper, Yangge Li, Sayan Mitra, Rajarshi Ray, Christian Schilling, Stefan Schupp, and Mark Wetzlinger (2020)","tags":["Reachability","ARCH-COMP"],"title":"ARCH-COMP20 Category Report: Continuous and Hybrid Systems with Linear Continuous Dynamics","type":"project"},{"authors":null,"categories":null,"content":"Publication ARCH-COMP20 Category Report: Continuous and Hybrid Systems with Nonlinear Dynamics. Luca Geretti, Julien Alexandre dit Sandretto, Matthias Althoff, Luis Benet, Alexandre Chapoutot, Xin Chen, Pieter Collins, Marcelo Forets, Daniel Freire, Fabian Immler, Niklas Kochdumper, David P. Sanders and Christian Schilling (2020) ARCH20. To appear in 7th International Workshop on Applied Verification of Continuous and Hybrid Systems. 7th International Workshop on Applied Verification of Continuous and Hybrid Systems (ARCH20), vol 74, pages 49\u0026ndash;75. 10.29007/zkf6.\nAbstract We present the results of a friendly competition for formal verification of continuous and hybrid systems with nonlinear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2020. This year, 6 tools Ariadne, CORA, DynIbex, Flow*, Isabelle/HOL, and JuliaReach (in alphabetic order) participated. These tools are applied to solve reachability analysis problems on six benchmark problems, two of them featuring hybrid dynamics. We do not rank the tools based on the results, but show the current status and discover the potential advantages of different tools.\nContributions In this report, we summarize the results of the fourth ARCH friendly competition on the reachability analysis of continuous and hybrid systems with nonlinear dynamics. Given a system defined by a nonlinear Ordinary Differential Equation (ODE) $\\dot{x} = f(x, t)$ along with an initial condition $x \\in X_0$, we apply the participating tools to prove properties of the state reachable set in a bounded time horizon. The techniques for solving such a problem are usually very sensitive to not only the nonlinearity of the dynamics but also the size of the initial set. This is also one of the main reasons why most of the tools require quite a lot of computational parameters. In this report, 6 tools Ariadne, CORA, DynIbex, Flow*, Isabelle/HOL, and JuliaReach participated in solving problems defined on four continuous and two hybrid benchmarks. The continuous benchmarks are the Production-Destruction system, the Coupled Van der Pol os- cillator, the Laub-Loomis model, and a controlled Quadrotor model. The hybrid benchmarks model a Lotka-Volterra system with a Tangential Crossing, and a Space Rendezvous system.\nFor the 2020 edition of the competition we introduced two new benchmarks: the Production- Destruction system and the Lotka-Volterra system with tangential crossing. The former is a continuous system aimed at identifying the stability of integration schemes. The latter intro- duces nonlinear guards and in particular tangential crossings. In addition, we extended the van der Pol oscillator to two coupled oscillators, introduced nondeterministic crossing in the Space Rendezvous system and performed some input sensitivity analysis for the Quadrotor system. The Laub-Loomis benchmark was not modified, in order to perform a direct comparison with results from the previous year (since the participants are the same).\nHow to cite @inproceedings{ARCH20:ARCH_COMP20_Category_Report_Continuous, author = {Luca Geretti and Julien Alexandre Dit Sandretto and Matthias Althoff and Luis Benet and Alexandre Chapoutot and Xin Chen and Pieter Collins and Marcelo Forets and Daniel Freire and Fabian Immler and Niklas Kochdumper and David P. Sanders and Christian Schilling}, title = {ARCH-COMP20 Category Report: Continuous and Hybrid Systems with Nonlinear Dynamics}, booktitle = {ARCH20. 7th International Workshop on Applied Verification of Continuous and Hybrid Systems (ARCH20)}, editor = {Goran Frehse and Matthias Althoff}, series = {EPiC Series in Computing}, volume = {74}, pages = {49--75}, year = {2020}, publisher = {EasyChair}, bibsource = {EasyChair, https://easychair.org}, issn = {2398-7340}, url = {https://easychair.org/publications/paper/nrdD}, doi = {10.29007/zkf6} }  ","date":1600992000,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1600992000,"objectID":"527105fddda29cb20cc5b37278672073","permalink":"https://juliareach.github.io/project/archcomp20_nln/","publishdate":"2020-09-25T00:00:00Z","relpermalink":"/project/archcomp20_nln/","section":"project","summary":"by Luca Geretti and Julien Alexandre Dit Sandretto and Matthias Althoff and Luis Benet and Alexandre Chapoutot and Xin Chen and Pieter Collins and Marcelo Forets and Daniel Freire and Fabian Immler and Niklas Kochdumper and David P. Sanders and Christian Schilling (2020)","tags":["Reachability","ARCH-COMP"],"title":"ARCH-COMP20 Category Report: Continuous and Hybrid Systems with Nonlinear Dynamics","type":"project"},{"authors":null,"categories":null,"content":"Publication Efficient reachability analysis of parametric linear hybrid systems with time-triggered transitions. Marcelo Forets, Daniel Freire, Christian Schilling, 2020. arXiv: 2006.12325.\nPresented in MEMOCODE'20: 18th ACM-IEEE International Conference on Formal Methods and Models for System Design .\nAbstract Efficiently handling time-triggered and possibly nondeterministic switches for hybrid systems reachability is a challenging task. In this paper we focus on periodically controlled systems with fast-switching controller dynamics, which often require simulation time scales of the order of nanoseconds. Accurate set-based computations for such systems with relatively large time horizons are expensive due to the accumulation of errors in the discrete transitions. We present an approach based on conservative set-based enclosure of the dynamics that can handle systems with uncertain parameters and inputs. We demonstrate our algorithm on the plant model of an experimental electro-mechanical braking system with periodic controller.\nContributions Timed systems play an important role in modeling and analyzing cyber-physical systems. In this work we consider a class of hybrid-automaton models with continuous dynamics and time-triggered discrete events following a periodic clock. We propose a reachability framework to compute an overapproximation of the states reachable by such systems.\nConventional techniques tightly integrate the computation of the continuous behavior and the discrete events. Our approach allows to separate these concerns for the model class considered here, which simplifies the analysis drastically in practice and allows us to plug in any reachability algorithm from the literature.\nAs a case study, we consider a parametric model of a cyber-physical system consisting of an experimental electro-mechanical brake and a software-implemented periodic controller. The model was originally described in earlier work by Strathmann and Oehlerking where the authors developed a simplified version of a nonlinear system. The model is representative of real challenges in the automotive industry and allows the application of formal methods during development. Computing the reachable states for this simplified model takes twelve hours using the previous approach, and less than a minute with our approach.\nThis paper makes the following original contributions:\n  We present an efficient algorithm for deterministic periodic time-triggered hybrid systems with uncertain parameters of the system dynamics or the initial conditions.\n  We extend the algorithm to the more difficult and new scenario of nondeterministic periodic discrete switches.\n  We demonstrate the efficiency of our algorithm on a model of an electro-mechanical brake system.\n  Presentation   Presentation slides (pdf) are available here.\n  A short video for MEMOCODE'20 is available here.\n  How to cite @article{forets2020efficient, title={Efficient reachability analysis of parametric linear hybrid systems with time-triggered transitions}, author={Forets, Marcelo and Freire, Daniel and Schilling, Christian}, journal={arXiv preprint arXiv:2006.12325}, year={2020} }  ","date":1590969600,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1590969600,"objectID":"62385185e2434755413066a027acea84","permalink":"https://juliareach.github.io/project/timetrigger/","publishdate":"2020-06-01T00:00:00Z","relpermalink":"/project/timetrigger/","section":"project","summary":"by Marcelo Forets, Daniel Freire, Christian Schilling (2020)","tags":["Reachability","Hybrid systems","Periodic controller"],"title":"Efficient reachability analysis of parametric linear hybrid systems with time-triggered transitions","type":"project"},{"authors":null,"categories":null,"content":"","date":1577836800,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1577836800,"objectID":"88872e52325d54ded5a39acf8e365fd8","permalink":"https://juliareach.github.io/software/rangeenclosures/","publishdate":"2020-01-01T00:00:00Z","relpermalink":"/software/rangeenclosures/","section":"software","summary":"A Julia package to compute Bernstein coefficients of multivariate polynomials","tags":null,"title":"RangeEnclosures.jl","type":"software"},{"authors":null,"categories":null,"content":"","date":1577836800,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1577836800,"objectID":"c1cb1c54d86495d4636fada5a395688a","permalink":"https://juliareach.github.io/software/reachabilitymodels/","publishdate":"2020-01-01T00:00:00Z","relpermalink":"/software/reachabilitymodels/","section":"software","summary":"A library of reachability models","tags":null,"title":"ReachabilityModels.jl","type":"software"},{"authors":null,"categories":null,"content":"Publication ARCH-COMP19 Category Report: Continuous and Hybrid Systems with Nonlinear Dynamics. Fabian Immler, Matthias Althoff, Luis Benet, Alexandre Chapoutot, Xin Chen, Marcelo Forets, Luca Geretti, Niklas Kochdumper, David P. Sanders and Christian Schilling (2019) ARCH19. 6th International Workshop on Applied Verification of Continuous and Hybrid Systems, vol 61, pages 41\u0026ndash;61 doi: 10.29007/bj1w.\nAbstract Contributions How to cite   ","date":1569369600,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1569369600,"objectID":"983ac409c454e61e1d2e80d575f1bff5","permalink":"https://juliareach.github.io/project/archcomp19_nln/","publishdate":"2019-09-25T00:00:00Z","relpermalink":"/project/archcomp19_nln/","section":"project","summary":"by Fabian Immler, Matthias Althoff, Luis Benet, Alexandre Chapoutot, Xin Chen, Marcelo Forets, Luca Geretti, Niklas Kochdumper, David P. Sanders and Christian Schilling (2019)","tags":["Reachability","ARCH-COMP"],"title":"ARCH-COMP19 Category Report: Continuous and Hybrid Systems with Nonlinear Dynamics","type":"project"},{"authors":null,"categories":null,"content":"Publication JuliaReach: a Toolbox for Set-Based Reachability. Sergiy Bogomolov, Marcelo Forets, Goran Frehse, Kostiantyn Potomkin, Christian Schilling. Published in Proceedings of HSCC'19: 22nd ACM International Conference on Hybrid Systems: Computation and Control (HSCC'19), see ACM link here. Get pdf from arXiv: 1901.10736.\nAbstract We present JuliaReach, a toolbox for set-based reachability analysis of dynamical systems. JuliaReach consists of two main packages: Reachability, containing implementations of reachability algorithms for continuous and hybrid systems, and LazySets, a standalone library that implements state-of-the-art algorithms for calculus with convex sets. The library offers both concrete and lazy set representations, where the latter stands for the ability to delay set computations until they are needed. The choice of the programming language Julia and the accompanying documentation of our toolbox allow researchers to easily translate set-based algorithms from mathematics to software in a platform-independent way, while achieving runtime performance that is comparable to statically compiled languages. Combining lazy operations in high dimensions and explicit computations in low dimensions, JuliaReach can be applied to solve complex, large-scale problems.\nHow to cite @inproceedings{bogomolov2019juliareach, title={JuliaReach: a toolbox for set-based reachability}, author={Bogomolov, Sergiy and Forets, Marcelo and Frehse, Goran and Potomkin, Kostiantyn and Schilling, Christian}, booktitle={Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control}, pages={39--44}, year={2019} }  ","date":1554076800,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1554076800,"objectID":"1115c9ac4b2ee1ff08466a42ea5d6672","permalink":"https://juliareach.github.io/project/juliareachtoolbox/","publishdate":"2019-04-01T00:00:00Z","relpermalink":"/project/juliareachtoolbox/","section":"project","summary":"by Sergiy Bogomolov, Marcelo Forets, Goran Frehse, Kostiantyn Potomkin, Christian Schilling (2019)","tags":["Reachability","Hybrid systems","Periodic controller"],"title":"JuliaReach: a Toolbox for Set-Based Reachability","type":"project"},{"authors":[],"categories":[],"content":"Create slides in Markdown with Wowchemy Wowchemy | Documentation\n Features  Efficiently write slides in Markdown 3-in-1: Create, Present, and Publish your slides Supports speaker notes Mobile friendly slides   Controls  Next: Right Arrow or Space Previous: Left Arrow Start: Home Finish: End Overview: Esc Speaker notes: S Fullscreen: F Zoom: Alt + Click PDF Export: E   Code Highlighting Inline code: variable\nCode block:\nporridge = \u0026quot;blueberry\u0026quot; if porridge == \u0026quot;blueberry\u0026quot;: print(\u0026quot;Eating...\u0026quot;)   Math In-line math: $x + y = z$\nBlock math:\n$$ f\\left( x \\right) = ;\\frac{{2\\left( {x + 4} \\right)\\left( {x - 4} \\right)}}{{\\left( {x + 4} \\right)\\left( {x + 1} \\right)}} $$\n Fragments Make content appear incrementally\n{{% fragment %}} One {{% /fragment %}} {{% fragment %}} **Two** {{% /fragment %}} {{% fragment %}} Three {{% /fragment %}}  Press Space to play!\nOne  Two  Three \n A fragment can accept two optional parameters:\n class: use a custom style (requires definition in custom CSS) weight: sets the order in which a fragment appears   Speaker Notes Add speaker notes to your presentation\n{{% speaker_note %}} - Only the speaker can read these notes - Press `S` key to view {{% /speaker_note %}}  Press the S key to view the speaker notes!\n Only the speaker can read these notes Press S key to view    Themes  black: Black background, white text, blue links (default) white: White background, black text, blue links league: Gray background, white text, blue links beige: Beige background, dark text, brown links sky: Blue background, thin dark text, blue links    night: Black background, thick white text, orange links serif: Cappuccino background, gray text, brown links simple: White background, black text, blue links solarized: Cream-colored background, dark green text, blue links   Custom Slide Customize the slide style and background\n{{\u0026lt; slide background-image=\u0026quot;/media/boards.jpg\u0026quot; \u0026gt;}} {{\u0026lt; slide background-color=\u0026quot;#0000FF\u0026quot; \u0026gt;}} {{\u0026lt; slide class=\u0026quot;my-style\u0026quot; \u0026gt;}}   Custom CSS Example Let\u0026rsquo;s make headers navy colored.\nCreate assets/css/reveal_custom.css with:\n.reveal section h1, .reveal section h2, .reveal section h3 { color: navy; }   Questions? Ask\nDocumentation\n","date":1549324800,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1549324800,"objectID":"0e6de1a61aa83269ff13324f3167c1a9","permalink":"https://juliareach.github.io/slides/example/","publishdate":"2019-02-05T00:00:00Z","relpermalink":"/slides/example/","section":"slides","summary":"An introduction to using Wowchemy's Slides feature.","tags":[],"title":"Slides","type":"slides"},{"authors":null,"categories":null,"content":"","date":1546300800,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1546300800,"objectID":"7aaf37253d7268ccc83f51209d22a65b","permalink":"https://juliareach.github.io/software/neuralnetworkanalysis/","publishdate":"2019-01-01T00:00:00Z","relpermalink":"/software/neuralnetworkanalysis/","section":"software","summary":"Methods to verify neural network control systems using reachability analysis","tags":null,"title":"NeuralNetworkAnalysis.jl","type":"software"},{"authors":null,"categories":null,"content":"Publication ARCH-COMP18 Category Report: Continuous and Hybrid Systems with Linear Continuous Dynamics. Matthias Althoff, Stanley Bak, Xin Chen, Chuchu Fan, Marcelo Forets, Goran Frehse, Niklas Kochdumper, Yangge Li, Sayan Mitra, Rajarshi Ray, Christian Schilling and Stefan Schupp (2018) ARCH18. 5th International Workshop on Applied Verification of Continuous and Hybrid Systems, 54: 23–52. doi: 10.29007/73mb.\nAbstract This report presents the results of a friendly competition for formal verification of continuous and hybrid systems with linear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2018. In its second edition, 9 tools have been applied to solve six different benchmark problems in the category for linear continuous dynamics (in alphabetical order): CORA, CORA/SX, C2E2, Flow*, HyDRA, Hylaa, Hylaa-Continuous, JuliaReach, SpaceEx, and XSpeed. This report is a snapshot of the current landscape of tools and the types of benchmarks they are particularly suited for. Due to the diversity of problems, we are not ranking tools, yet the presented results probably provide the most complete assessment of tools for the safety verification of continuous and hybrid systems with linear continuous dynamics up to this date.\nContributions This report summarizes results obtained in the 2018 friendly competition of the ARCH workshop for verifying hybrid systems with linear continuous dynamics $$ \\dot{x}(t) = Ax(t) + Bu(t), $$ where $A \\in \\mathbb{R}^{n \\times n}$, $x \\in \\mathbb{R}^n$, $B \\in \\mathbb{R}^{n \\times m}$, and $u \\in \\mathbb{R}^m$. Participating tools are summarized in Sec. 2. The results of our selected benchmark problems are shown in Sec. 3 and are obtained on the tool developers’ own machines. Thus, one has to factor in the computational power of the processors used, summarized in Appendix A, as well as the efficiency of the programming language of the tools. The goal of the friendly competition is not to rank the results, but rather to present the landscape of existing solutions in a breadth that is not possible with scientific publications in classical venues. Such publications would typically require the presentation of novel techniques, while this report showcases the current state-of-the-art tools. For all results reported by each participant, we have run an independent repeatability evaluation. The selection of the benchmarks has been conducted within the forum of the ARCH website (cps-vo.org/group/ARCH), which is visible for registered users and registration is open for anybody. All tools presented in this report use some form of reachability analysis. This, however, is not a constraint set by the organizers of the friendly competition. We hope to encourage further tool developers to showcase their results in future editions.\nHow to cite @inproceedings{ARCH18:ARCH_COMP18_Category_Report_Continuous, author = {Matthias Althoff and Stanley Bak and Xin Chen and Chuchu Fan and Marcelo Forets and Goran Frehse and Niklas Kochdumper and Yangge Li and Sayan Mitra and Rajarshi Ray and Christian Schilling and Stefan Schupp}, title = {ARCH-COMP18 Category Report: Continuous and Hybrid Systems with Linear Continuous Dynamics}, booktitle = {ARCH18. 5th International Workshop on Applied Verification of Continuous and Hybrid Systems}, editor = {Goran Frehse}, series = {EPiC Series in Computing}, volume = {54}, pages = {23--52}, year = {2018}, publisher = {EasyChair}, bibsource = {EasyChair, https://easychair.org}, issn = {2398-7340}, url = {https://easychair.org/publications/paper/4cGr}, doi = {10.29007/73mb}}  ","date":1537142400,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1537142400,"objectID":"3d5557c51c77c9afc64c5cdb25e0581b","permalink":"https://juliareach.github.io/project/archcomp18_aff/","publishdate":"2018-09-17T00:00:00Z","relpermalink":"/project/archcomp18_aff/","section":"project","summary":"by Matthias Althoff, Stanley Bak, Xin Chen, Chuchu Fan, Marcelo Forets, Goran Frehse, Niklas Kochdumper, Yangge Li, Sayan Mitra, Rajarshi Ray, Christian Schilling and Stefan Schupp (2018)","tags":["Reachability","ARCH-COMP"],"title":"ARCH-COMP18 Category Report: Continuous and Hybrid Systems with Linear Continuous Dynamics","type":"project"},{"authors":null,"categories":null,"content":"Publication Reach Set Approximation through Decomposition with Low-dimensional Sets and High-dimensional Matrices. Sergiy Bogomolov, Marcelo Forets, Goran Frehse, Frédéric Viry, Andreas Podelski and Christian Schilling (2018) HSCC'18 Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control: 41–50. See the ACM Digital Library link, or the arXiv: 1801.09526.\nAbstract Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety. Although progress has been made in the development of efficient algorithms for affine dynamical systems, available algorithms still lack scalability to ensure their wide adoption in the industrial setting. While modern linear algebra packages are efficient for matrices with tens of thousands of dimensions, set-based image computations are limited to a few hundred. We propose to decompose reach set computations such that set operations are performed in low dimensions, while matrix operations like exponentiation are carried out in the full dimension. Our method is applicable both in dense and discrete-time settings. For a set of standard benchmarks, it shows a speed-up of up to two orders of magnitude compared to the respective state-of-the-art tools, with only modest losses in accuracy. For the dense-time case, we show an experiment with more than 10,000 variables, roughly two orders of magnitude higher than possible with previous approaches.\nContributions We present a new method to solve the reachability problem for affine dynamical systems with nondeterministic inputs and experimentally show that it is highly scalable under modest loss of accuracy.\nMore precisely:\n We provide a new decomposition approach to solve the set-based recurrence:  $$ \\mathcal{X}(k+1) = \\Phi \\mathcal{X}(k) \\oplus \\mathcal{V}(k),\\qquad k = 0, 1,\\ldots, N $$\n  We analyze the approximation error.\n  We address both the dense time and the discrete time reach- ability problem for general linear time-invariant systems.\n  We implement our approach efficiently and demonstrate its scalability on real engineering benchmarks. The tool, source code, and benchmark scripts are publicly available.\n  How to cite @inproceedings{bogomolov2018reach, title={Reach set approximation through decomposition with low-dimensional sets and high-dimensional matrices}, author={Bogomolov, Sergiy and Forets, Marcelo and Frehse, Goran and Viry, Fr{\\'e}d{\\'e}ric and Podelski, Andreas and Schilling, Christian}, booktitle={Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)}, pages={41--50}, year={2018} }  ","date":1522540800,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1522540800,"objectID":"fa3b25c7ebc384cae327ec4030868985","permalink":"https://juliareach.github.io/project/bffpsv18/","publishdate":"2018-04-01T00:00:00Z","relpermalink":"/project/bffpsv18/","section":"project","summary":"by Sergiy Bogomolov, Marcelo Forets, Goran Frehse, Frédéric Viry, Andreas Podelski and Christian Schilling (2018)","tags":["Reachability","Hybrid systems","Periodic controller"],"title":"Reach Set Approximation through Decomposition with Low-dimensional Sets and High-dimensional Matrices","type":"project"},{"authors":null,"categories":null,"content":"","date":1461715200,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1461715200,"objectID":"fc40296106e4609cf2e8e77b9e55bc41","permalink":"https://juliareach.github.io/software/mathematicalsystems/","publishdate":"2016-04-27T00:00:00Z","relpermalink":"/software/mathematicalsystems/","section":"software","summary":"Systems definitions in Julia","tags":null,"title":"MathematicalSystems.jl","type":"software"},{"authors":null,"categories":null,"content":"","date":1136073600,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1136073600,"objectID":"3bf56fe54fe6b655748274956cb421c0","permalink":"https://juliareach.github.io/software/bernsteinexpansions/","publishdate":"2006-01-01T00:00:00Z","relpermalink":"/software/bernsteinexpansions/","section":"software","summary":"A Julia package to compute Bernstein coefficients of multivariate polynomials","tags":null,"title":"BernsteinExpansions.jl","type":"software"},{"authors":null,"categories":null,"content":"","date":1104537600,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1104537600,"objectID":"5ee385644754194fea39a234f4e8ca11","permalink":"https://juliareach.github.io/software/mathematicalpredicates/","publishdate":"2005-01-01T00:00:00Z","relpermalink":"/software/mathematicalpredicates/","section":"software","summary":"Predicate definitions in Julia","tags":null,"title":"MathematicalPredicates.jl","type":"software"}]