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 specifications 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 specifications of objects as having both algebraic and coalgebraic aspects.
CITATION STYLE
Malcolm, G. (1996). Behavioural equivalence, bisimulation, and minimal realisation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1130, pp. 360–378). Springer Verlag. https://doi.org/10.1007/3-540-61629-2_53
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