Generic Trace Semantics via Coinduction

Details Generic Trace Semantics via Coinduction Generic Trace Semantics via Coinduction

2007-10-12

arxiv.org/abs/0710.2505v2

LMCS 3 (4:11) 2007

Computer Science

Logic in Computer Science

To appear in Logical Methods in Computer Science. 36 pages

Scientific paper

10.2168/LMCS-3(4:11)2007

Trace semantics has been defined for various kinds of state-based systems, notably with different forms of branching such as non-determinism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these "trace semantics," namely coinduction in a Kleisli category. This claim is based on our technical result that, under a suitably order-enriched setting, a final coalgebra in a Kleisli category is given by an initial algebra in the category Sets. Formerly the theory of coalgebras has been employed mostly in Sets where coinduction yields a finer process semantics of bisimilarity. Therefore this paper extends the application field of coalgebras, providing a new instance of the principle "process semantics via coinduction."

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