Bisimulations and abstraction homomorphisms
Journal of Computer and System Sciences
Introducing a calculus of trees
TAPSOFT '91 Proceedings of the international joint conference on theory and practice of software development on Colloquium on trees in algebra and programming (CAAP '91): vol 1
Elementary categories, elementary toposes
Elementary categories, elementary toposes
Communication and Concurrency
A Calculus of Communicating Systems
A Calculus of Communicating Systems
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In this paper a we give a semantics for SCCS using the constructions of the topos of labelled trees. The semantics accounts for all aspects of the original formulation of SCCS, including unbounded non-determinism. Then, a partial solution to the problem of characterizing bisimulation in terms of a class of morphisms is proposed. We define a class of morphisms of the topos of trees, called conflict preserving, such that two trees T and U are bisimilar iff there is a pair of conflict preserving morphisms f : T → U and g : U → T such that fgf = f and gfg = g. It is the first characterization which does not require the existence of a third quotient object. The results can be easily extended to more general transition systems.