Modal Observation Equivalence of Processes

This paper shows that many simulation equivalences over processes can be characterised by a single parameterised modal logic formula. Strong bisimulation equivalence was shown by Milner to be characterised in this way. This paper shows that simulation, complete simulation, ready simulation, 2-nested simulation, weak bisimulation and congruence can also be characterised in this way. The paper constructs a template which can be used to generate a parametrised modal formula which is guaranteed to characterise a 'sensible' simulation equivalence. Two infinite families of simulation equivalences are characterised in this way, both of which converge to strong bisimulation. The paper defines a similar template for weak simulation equivalences. This template is used to construct an infinite family of equivalences which converges to weak bisimulation equivalence, and another infinite family which converges to congruence.

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