1. Formal Methods in software development
a.a.2017/2018
Prof.Anna Labella
1/2/2019

2. Proving Equivalences The bisimulation proof method:
To establish P  Q:
Identify a relation S such that P S Q
Prove that S is a weak bisimulation relation
This is the canonical method
There are other methods for process verification:
Modal logic specification/proof (see later)
Equational reasoning (rewriting method: see later)
1/2/2019

3. Bisimilarity as a maximal fixed point
Let us take Q  Q to start with, then calculate
F(Q  Q) ={ (q1,q2) | q1  q1’ implies q2  q2’ and viceversa}.
By iterating the procedure, we obtain a decreasing chain
…F4(Q  Q)  F3(Q  Q)  F2(Q  Q)  F(Q  Q)
We can apply Tarski’s theorem and obtain a maximal fixed point
S  Q  Q. The relation S is a strong bisimulation.
The same holds for weak bisimulation relation defining
F(Q  Q) ={ (q1,q2) | q1  q1’ implies q2  q2’ and viceversa}
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9. We will give a language, the so-called
Hennessy-Milner logic, which describes
observations/experiments on LTSs
1/2/2019

10. HennessyMilnerLogic.pdf
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