Latella, Diego and Massink, Mieke and De Vink, Erik P - Bisimulation of Labelled State-to-Function Transition Systems Coalgebraically

lmcs:1617 - Logical Methods in Computer Science, December 22, 2015, Volume 11, Issue 4
Bisimulation of Labelled State-to-Function Transition Systems Coalgebraically

Authors: Latella, Diego and Massink, Mieke and De Vink, Erik P

Labeled state-to-function transition systems, FuTS for short, are characterized by transitions which relate states to functions of states over general semirings, equipped with a rich set of higher-order operators. As such, FuTS constitute a convenient modeling instrument to deal with process languages and their quantitative extensions in particular. In this paper, the notion of bisimulation induced by a FuTS is addressed from a coalgebraic point of view. A correspondence result is established stating that FuTS-bisimilarity coincides with behavioural equivalence of the associated functor. As generic examples, the equivalences underlying substantial fragments of major examples of quantitative process algebras are related to the bisimilarity of specific FuTS. The examples range from a stochastic process language, PEPA, to a language for Interactive Markov Chains, IML, a (discrete) timed process language, TPC, and a language for Markov Automata, MAL. The equivalences underlying these languages are related to the bisimilarity of their specific FuTS. By the correspondence result coalgebraic justification of the equivalences of these calculi is obtained. The specific selection of languages, besides covering a large variety of process interaction models and modelling choices involving quantities, allows us to show different classes of FuTS, namely so-called simple FuTS, combined FuTS, nested FuTS, and general FuTS.


Source : oai:arXiv.org:1511.05866
DOI : 10.2168/LMCS-11(4:16)2015
Volume: Volume 11, Issue 4
Published on: December 22, 2015
Submitted on: September 16, 2015
Keywords: Computer Science - Logic in Computer Science


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