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Concurrent Systems/notes/13 - Weak Bisimilarity.md

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+The equivalence studied up to now is quite discriminating, in the sense that it distinguishes, for example, τ.P and τ.τ.P.
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+- If an external observer can count the number of non-observable actions (i.e., the τ’s), this distinction makes sense.
+- If we assume that an observer cannot access any internal information of the system, then this distinction is not acceptable.
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+The idea of the new equivalence is to ignore (some) τ’s:
+- a visible action must be replied to with the same action, possibly together with some internal actions
+- an internal action must be replied to by a (possibly empty) sequence of internal actions.
+
+$P \implies P'$ if and only if there exist $P_{0}, P_{1},\dots,P_{k}$ (for $k \geq 0$) such that $P=P_{0} \xrightarrow{\tau} P_{1} \xrightarrow{\tau}$