38 lines
1.5 KiB
Markdown
38 lines
1.5 KiB
Markdown
We shall only consider finite processes (processes without recursive definitions)
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- a limited handling of recursion is possible
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- deciding bisimilarity for general processes is undecidable
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Inference system = axioms + inference rules
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- soundness: whatever I infer is correct (i.e., bisimiar)
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- completeness: whatever is bisimilar, it can be inferred
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#### Axioms & Rules for Strong Bisimilarity
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quite obvious.
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basically we can let the left or the right process evolve, leaving the other unchanged, or they can synchronize.
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- if a process does not perform any action, a restriction won't do anything
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- ...
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$P$ 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.
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**Lemma:** $\forall P \exists P'$* in standard form such that $\vdash P = P'$
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*Proof:* by induction on the structure of P.
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**Base case:** $P \triangleq 0$. It suffices to consider $P' \triangleq 0$ and conclude reflexivity.
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**Inductive step:** we have to consider three cases.
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replacing one by one every continuation with its standard form, obtaining standard form.
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