16 lines
No EOL
1 KiB
Markdown
16 lines
No EOL
1 KiB
Markdown
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.
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- 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:
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- a visible action must be replied to with the same action, possibly together with some internal actions
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- an internal action must be replied to by a (possibly empty) sequence of internal actions.
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We define the relation $\implies$ as:
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$P \implies P'$ if and only if there exist $P_{0}, P_{1},\dots,P_{k}$ (for $k \geq 0$) such that $P=P_{0} \xrightarrow{\tau} P_{1} \xrightarrow{\tau}\dots\xrightarrow{\tau}Pk=P'$
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relation $\xRightarrow{\hat{\alpha}}$:
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- if $\alpha=\tau$ then $\xRightarrow{\hat{\alpha}}\triangleq\implies$
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- otherwise $\xRightarrow{\hat{\alpha}}\triangleq\implies\xrightarr$ |