Kerstan, Henning and König, Barbara - Coalgebraic Trace Semantics for Continuous Probabilistic Transition Systems

lmcs:859 - Logical Methods in Computer Science, December 4, 2013, Volume 9, Issue 4
Coalgebraic Trace Semantics for Continuous Probabilistic Transition Systems

Authors: Kerstan, Henning and König, Barbara

Coalgebras in a Kleisli category yield a generic definition of trace semantics for various types of labelled transition systems. In this paper we apply this generic theory to generative probabilistic transition systems, short PTS, with arbitrary (possibly uncountable) state spaces. We consider the sub-probability monad and the probability monad (Giry monad) on the category of measurable spaces and measurable functions. Our main contribution is that the existence of a final coalgebra in the Kleisli category of these monads is closely connected to the measure-theoretic extension theorem for sigma-finite pre-measures. In fact, we obtain a practical definition of the trace measure for both finite and infinite traces of PTS that subsumes a well-known result for discrete probabilistic transition systems. Finally we consider two example systems with uncountable state spaces and apply our theory to calculate their trace measures.


Source : oai:arXiv.org:1310.7417
DOI : 10.2168/LMCS-9(4:16)2013
Volume: Volume 9, Issue 4
Published on: December 4, 2013
Submitted on: January 15, 2013
Keywords: Computer Science - Logic in Computer Science


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