master-degree-notes/Concurrent Systems/notes/14.md

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We shall only consider finite processes (processes without recursive definitions)
- a limited handling of recursion is possible
- deciding bisimilarity for general processes is undecidable
Inference system = axioms + inference rules
- soundness: whatever I infer is correct (i.e., bisimiar)
- completeness: whatever is bisimilar, it can be inferred
#### Axioms & Rules for Strong Bisimilarity
![350](../../Pasted%20image%2020250429082812.png)
quite obvious.
![350](../../Pasted%20image%2020250429082905.png)
basically we can let the left or the right process evolve, leaving the other unchanged, or they can synchronize.
![350](../../Pasted%20image%2020250429083129.png)
- if a process does not perform any action, a restriction won't do anything
- ...
![350](../../Pasted%20image%2020250429083455.png)
![](../../Pasted%20image%2020250429083535.png)
$P$ is in standard form if and only if $P \triangleq \sum_{i}\alpha_{i}P_{i}$ and $\forall_{i}P_{i}$ is in standard form.