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Marco Realacci 2025-04-14 08:49:56 +02:00
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Concurrent Systems/notes/11 - LTSs and Bisimulation.md
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@ -60,4 +60,10 @@ If S contained one among (p1,q1) or (p1,q2), then it would not be a simulation:
p0 is simulated by q0: $$S = {(p0, q0), (p1, q2), (p2, q3)}$$
q0 is simulated by p0: $$S′ ={(q0,p0),(q1,p1),(q2,p1),(q3,p2)}$$
However, p0 and q0 are not bisimilar: the transition q0 -> a -> q1 is not bisimulable by any transition from p0 (ndeed, p0 –a–> p1 does not suffice, because p1 can perform a b and so cannot be bisimilar to q1).
However, p0 and q0 are not bisimilar: the transition q0 -> a -> q1 is not bisimulable by any transition from p0 (ndeed, p0 –a–> p1 does not suffice, because p1 can perform a b and so cannot be bisimilar to q1).
#### Bisimulation is NOT isomorfism
![](../../Pasted%20image%2020250414084615.png)
$S = \{(p0,q0), (p1,q1), (p2,q1), (p0,q2)\}$
$S^{−1} = \{(q0,p0), (q1,p1), (q1,p2), (q2,p0)\}$