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Update problem.md
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docs/electro-drivers/problem.md

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@@ -26,8 +26,8 @@ The problem statement is to provide:
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Functional problem formula:
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$$
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P_{functional} = \{ P_{I/O\ Emulation\ of\ IO-2\ interface\ over\ I/O-1\ interface},\
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P_{Compatible\ I/O\ architectures} \}
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P_{functional} = \\{ P_{I/O\ Emulation\ of\ IO-2\ interface\ over\ I/O-1\ interface},\\
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P_{Compatible\ I/O\ architectures} \\}
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$$
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> [!NOTE]
@@ -43,10 +43,10 @@ The final sub-problems set is a subset of the original bulk set presented in **S
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Functional problems decomposition formula:
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$$
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P_{functional} = \{ P_{I/O\ Emulator\ Interface},\
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P_{functional} = \\{ P_{I/O\ Emulator\ Interface},\
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P_{I/O\ Emulated\ Interface},\
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P_{Emulation\ Kernel\ Engine},\
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P_{Emulation\ User\ Engine} \}
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P_{Emulation\ User\ Engine} \\}
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$$
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> [!NOTE]
@@ -63,7 +63,7 @@ These parts of the problem are not playing an explicit role in the functional re
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Non-functional problems formula:
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$$
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P_{Non-functional} = \{
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P_{Non-functional} = \\{
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P_{I/O\ resources\ shared\ acquisition},\
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P_{I/O\ Locked\ threaded\ init},\
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P_{I/O\ Locked\ error\ handling},\
@@ -73,7 +73,7 @@ P_{Programmed\ threaded\ interrupted\ I/O},\
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P_{I/O\ resources\ release},\
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P_{I/O\ device\ de-init},\
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P_{Linux\ VFS},\
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P_{Emulation\ VM} \}
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P_{Emulation\ VM} \\}
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$$
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---
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* Let $M_{IO}(p)$ be a set of ordered pairs that maps a functional problem to other non-functional problems; such that $p$ is an input/output interface problem for a physical or virtual I/O device.
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$$
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M_{IO}(p) = \{
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M_{IO}(p) = \\{
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(P_{p}, P_{I/O\ resources\ shared\ acquisition}),\
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(P_{p}, P_{I/O\ Locked\ threaded\ init}),\
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(P_{p}, P_{I/O\ Locked\ error\ handling}),\
@@ -97,21 +97,21 @@ M_{IO}(p) = \{
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(P_{p}, P_{I/O\ resources\ release}),\
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(P_{p}, P_{I/O\ device\ de-init}),\
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(P_{p}, P_{Linux\ VFS}),\
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(P_{p}, P_{Emulation\ VM}) \}
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(P_{p}, P_{Emulation\ VM}) \\}
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$$
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* Let $M_{Engine}(p)$ be a set of ordered pairs that maps a functional problem to other non-functional problems; such that $p$ is an engine interface problem for providing the emulation of an I/O interface over the other; an engine could be a **user-space** engine or a **kernel-space** engine.
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$$
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M_{Engine}(p) = \{
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M_{Engine}(p) = \\{
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(P_{p}, P_{I/O\ R/W\ Clock\ Cycle}),\
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(P_{p}, P_{Linux\ VFS}),\
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(P_{p}, P_{Char/Block\ Devices}),\
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(P_{p}, P_{Emulation\ VM}),\
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(P_{p}, P_{I/O\ Operation\ Lifecycle}) \}
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(P_{p}, P_{I/O\ Operation\ Lifecycle}) \\}
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$$
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## 2) Design Implications:
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