vault backup: 2025-04-29 09:18:47

Concurrent Systems/notes/14.md

@@ -47,4 +47,10 @@ The behavior of such a server can be implemented by three processes in parallel:
 - another one effectively sends the message (through the restricted action *put*) and waits for the signal of message reception (through the restricted action *go*)
 - the last one gives back to the user the outcome of the sending
 
-$$S \triangleq send.\overline{put} \quad M \triangleq send.\overline{put}$$
+$$S \triangleq send.\overline{put} \quad M \triangleq put.\overline{go} \quad R \triangleq go.\overline{rcv}$$
+$$Impl \triangleq (S|M|R)\setminus\{put, go\}$$
+exercise: prove the weak bisimilarity
+
+Let us consider the parallel of processes M and R, by using the axiom for parallel, we have $$\vdash M|R=put.(\overline{go}|R)+go.(M|\overline{rcv})$$
+By using the same axiom to the parallel of the three processes, we obtain
+$$\vdash S|(M|R)=send.(\overline{put}|(M|R))+put.(\overline{go})$$