Modal Observation Equivalence of Processes

This paper shows that many simulation equivalences over processes can be characterised by a single parameterised modal logic formula. For many equivalences there is a parameterised modal logic formula f(t) such that for every pair of processes P and Q, P Q if and only if P j= f(Q). For any speci c P the formula f(P ) becomes a x point formula of the normal modal logic K . Strong bisimulation equivalence was shown by Milner [16] 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 parameterised modal formula which is guaranteed to characterise a `sensible' simulation equivalence. Two in nite families of simulation equivalences are characterised in this way, both of which converge to . The paper de nes a similar template for weak simulation equivalences. This template is used to construct an in nite family of equivalences which converges to weak bisimulation equivalence, and another in nite family which converges to congruence. Any equivalence relation which contains can be characterised in a weaker sense by K . If contains , then for each P there is an f P 2 K such that P Q i j= f P $ f Q. The paper proves this for arbitrary via the axiom of choice. The paper gives a speci c construction for such an f P for trace, complete trace, failure trace, ready trace and possible future equivalence .