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Marco Realacci 2025-04-29 09:18:47 +02:00
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8
Concurrent Systems/notes/14.md
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@ -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*) - 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 - 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
$$\vdash S|(M|R)=send.(\overline{put}|(M|R))+put.(\overline{go})$$