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Marco Realacci 2025-04-29 09:23:47 +02:00
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9
Concurrent Systems/notes/14.md
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@ -53,4 +53,11 @@ 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
$$\vdash S|(M|R)=send.(\overline{put}|(M|R))+put.(\overline{go})$$
$$\vdash S|(M|R)=send.(\overline{put}|(M|R))+put.(\overline{go}|R|S)+go.(\overline{rcv}|S|M)$$
By restricting *put* and *go*, and by using the second axiom for restriction, we have that:
![](../../Pasted%20image%2020250429091959.png)
We now apply the third axiom for restriction to the three summands:
![](../../Pasted%20image%2020250429092055.png)
![](../../Pasted%20image%2020250429092305.png)