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 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."Comment: To appear in Logical Methods in Computer Science. 36 page

Abstract SOS 2004 Preliminary Version From Bialgebraic Semantics to Congruence Formats

A general and abstract framework to defining congruence formats for various process equivalences is presented. The framework extends bialgebraic techniques of Turi and Plotkin with an abstract coalgebraic approach to process equivalence, based on a notion of test suite. The resulting technique is illustrated on the example of completed trace equivalence. Rather than providing formal proofs, the paper is guiding the reader through the process of deriving a congruence format in the test suite approach. Key words: process algebra, structural operational semantics, congruence format, bialgebraic semantic