Generic Trace Semantics via Coinduction

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 Kle...

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Bibliographic Details
Published inLogical methods in computer science Vol. 3, Issue 4
Main Authors Hasuo, Ichiro, Jacobs, Bart, Sokolova, Ana
Format Journal Article
LanguageEnglish
Published Logical Methods in Computer Science e.V 19.11.2007
Subjects
computer science - logic in computer science
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Summary: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."
ISSN:1860-5974
1860-5974
DOI:10.2168/LMCS-3(4:11)2007