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Concurrent Systems/notes/14 Checking bisimilarity, an inference system.md
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@ -79,10 +79,10 @@ exercise: prove the weak bisimilarity between the spec and the implementation.
Let us consider the parallel of processes M and R, by using the axiom for parallel, we have $$\vdash M|R=put.(\overline{go}|R)+go.(M|\overline{rcv})$$ 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 By using the same axiom to the parallel of the three processes, we obtain
$$\vdash S|(M|R)=send.(\overline{put}|(M|R))+put.(\overline{go}|R|S)+go.(\overline{rcv}|S|M)$$ $$\vdash S|(M|R)=send.(\overline{put}|(M|R))+put.(\overline{go}|R|S)+go.(\overline{rcv}|S|M)$$
By restricting *put* and *go*, and by using the second axiom for restriction, we have that (spostiamo la res): By restricting *put* and *go*, and by using the second axiom for restriction, we have that (spostiamo la restrizione dentro):
![](images/Pasted%20image%2020250429091959.png) ![](images/Pasted%20image%2020250429091959.png)
We now apply the third axiom for restriction to the three summands: We now apply the third axiom for restriction to the three summands (effettivamente applichiamo la restrizione):
![](images/Pasted%20image%2020250429092055.png) ![](images/Pasted%20image%2020250429092055.png)
![](images/Pasted%20image%2020250429092305.png) ![](images/Pasted%20image%2020250429092305.png)
![](images/Pasted%20image%2020250429092543.png) ![](images/Pasted%20image%2020250429092543.png)