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Marco Realacci 2025-05-05 10:04:15 +02:00
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.obsidian/workspace.json vendored
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@ -213,10 +213,10 @@
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"Concurrent Systems/notes/8 - Enhancing Liveness Properties.md", "Concurrent Systems/notes/8 - Enhancing Liveness Properties.md",
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Concurrent Systems/notes/15 - A formal language for LTSs.md
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@ -90,3 +90,9 @@ indeed, P1 can simulate P2 and viceversa, but the simulations are not bisimulati
##### A negation and conjunction-free logic ##### A negation and conjunction-free logic
![](../../Pasted%20image%2020250505095743.png) ![](../../Pasted%20image%2020250505095743.png)
### A Logic for Weak Bisimilarity
Very similar. $$\phi := TT | \lnot \phi | \phi \land \phi|\ll\gg a \phi \quad where \space a \in Action$$
The only difference is the diamond operator, that here is turned into <<>>a.
This is very similar to the difference between the definition of weak and strong simulation, where the former is obtained from the latter by replacing $\xrightarrow{a}$ with $\xRightarrow{\hat{a}}$. Satisfiability of this new operator is expectable: $$P \models \ll\gg a\phi \iff \exists P' : P \xRightarrow{P'} \land P' \models \phi$$