diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 251b622..6581465 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -213,6 +213,7 @@ }, "active": "56150e6df7869900", "lastOpenFiles": [ + "Pasted image 20250428085837.png", "Concurrent Systems/slides/class 13.pdf", "Concurrent Systems/notes/13 - Weak Bisimilarity.md", "Pasted image 20250428085410.png", diff --git a/Concurrent Systems/notes/13 - Weak Bisimilarity.md b/Concurrent Systems/notes/13 - Weak Bisimilarity.md index da46ebb..bed02ee 100644 --- a/Concurrent Systems/notes/13 - Weak Bisimilarity.md +++ b/Concurrent Systems/notes/13 - Weak Bisimilarity.md @@ -76,4 +76,12 @@ There is only one special and only one general machine that the workers have to where rg and rs are used to require the general/special machine, lg and ls are used to leave the general/special machine, and S and G implement a semaphore on the two different machines. The resulting system is given by: -$$Workers \triangleq (W|W|G|S) \setminus_{\{rg,rs,lg,ls \}}$$ \ No newline at end of file +$$Workers \triangleq (W|W|G|S) \setminus_{\{rg,rs,lg,ls \}}$$ +We now want to show that: +$$Factory \approx Workers$$ +i.e., that the specification and the implementation of the factory behave the same (apart from internal actions). + +Let N denote {rg,rs,lg,ls} and x,y ∊ {E,M,D} +We can prove that the following relation is a weak bisimulation: +![](../../Pasted%20image%2020250428085837.png) + diff --git a/Pasted image 20250428085837.png b/Pasted image 20250428085837.png new file mode 100644 index 0000000..40c2ffa Binary files /dev/null and b/Pasted image 20250428085837.png differ