Behavioural Equivalence, Bisimulation, and Minimal Realisation

This paper examines three important topics in computer science: behavioural equivalence, bisimulation, and minimal realisation of automata, and discusses the relationships that hold between them. Central to all three topics is a notion of equivalence of behaviour, and by taking a coalgebraic approach to algebraic speciications we show that bisimulation is`the same as' behavioural equivalence. Moreover, we show that a particular construction for minimal realisation of behaviour corresponds to a proof technique for proving behavioural equivalence. We also argue that it is useful to consider algebraic speciications of objects as having both algebraic and coalgebraic aspects.