Strong Bisimulation

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Fact ~ is the largest strong bisimulation, that is, ~ is a strong bisimulation and includes any other such. Assume that each S i (i=1,2,…) is a strong bisimulation. Then U S is a strong bisimulation. i∈ I i Let each S i (i=1,2,…) be a strong bisimulation. We have to show that U S is a strong bisimulation. i∈ I i Let (p,q) ∈ U S i∈ I i . If p α ⎯⎯→ p' , then since (p,q) ∈ S i , 1 ≤ i ≤ n, there exists a q’ ∈ S i with q α ⎯⎯→ q' and (p’,q’) ∈ S i and (p’,q’) ∈ U S . By symmetry, the converse holds as well. i∈ I i 51
Bisimulation - Summary Bisimulation is an equivalence relation defined over a labeled transition system, which respects non-determinism. The bisimulation technique can be used to compare the observable behavior of interacting systems. Note: Strong bisimulation does not cover unobservable behavior, which is present in systems that have operators to define reaction (that is, internal actions). 52
Page 1 and 2: Strong Bisimulation Overview • Ac
Page 3 and 4: General Automaton a,b,c b,c q3 a,b
Page 5 and 6: LTS and Automaton An LTS can be tho
Page 7 and 8: Strong Simulation - Definition Let
Page 9 and 10: Defining S If we define S = {(p0, q
Page 11 and 12: Diagrams The condition for S to be
Page 13 and 14: Working With Simulations What do we
Page 15 and 16: Linking States b p0 b a a p1 p2 a a
Page 17 and 18: Reflexivity Let Q be a process and
Page 19: Transitivity S 1 ° S 2 = {(p, r) |

Strong Bisimulation

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