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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:
-$$Workers \triangleq (W|W|G|S) \setminus_{\{rg,rs,lg,ls  \}}$$
+$$Workers \triangleq (W|W|G|S) \setminus_{\{rg,rs,lg,ls  \}}$$
+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)
+