vault backup: 2025-04-30 13:27:49
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@ -10,7 +10,7 @@ $$S_{2}^{(2)} \triangleq v \cdot S_{1}^{(2)}$$
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If we consider S(2) as the specification of the expected behavior of a binary semaphore and S(1) | S(1) as its concrete implementation, we can show that $$S^{(1)}|S^{(1)} \space \textasciitilde \space S^{2}$$
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This means that the implementation and the specification do coincide. To show this equivalence, it suffices to show that following relation is a bisimulation:
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## Restrictions
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**Proposition:** $a.P \textbackslash a ∼ 0$
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@ -50,7 +50,7 @@ One of the main aims of an equivalence notion between processes is to make equat
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**This feature on an equivalence makes it a *congruence***
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Not all equivalences are necessarily congruences (even though most of them are).
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To properly define a congruence, we first need to define an execution context, and then what it means to run a process in a context. Intuitively:
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where C is a context (i.e., a process with a hole ☐), P is a process, and $C[P]$ denotes filling the hole with P
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