Abstract

Abstract. We give a general framework relating a branching time relation on nodes of a transition system to a final coalgebra for a suitable endofunctor. Examples of relations treated by our theory include bisimilarity (a well known example), similarity, upper and lower similarity for transition systems with divergence, and nested similarity. Our results describe firstly how to characterize the relation in terms of a given final coalgebra, and secondly how to construct a final coalgebra using the relation. Our theory uses a notion of “relator ” based on earlier work of Thijs. But whereas a relator must preserve binary composition in Thijs ’ framework, it only laxly preserves composition in ours. It is this weaker requirement that allows nested similarity to be an example. 1

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