# Coalgebraic Trace Semantics for Probabilistic Transition Systems ...

## Reference

Henning Kerstan and Barbara König.

Coalgebraic trace semantics for probabilistic transition systems based on measure theory. Technical Report 2012-02, Abteilung für Informatik und Angewandte Kognitionswissenschaft, Universität Duisburg-Essen, jun 2012.

## Abstract

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.

## Keywords:

trace semantics, probabilistic transition system

## Suggested BibTeX entry:

@

techreport{KK12b,

author= {Henning Kerstan and Barbara K{\"o}nig},

institution= {Abteilung f{\"u}r Informatik und Angewandte Kognitionswissenschaft, Universit{\"a}t Duisburg-Essen},

month= {jun},

number= {2012-02},

title= {Coalgebraic Trace Semantics for Probabilistic Transition Systems Based on Measure Theory},

year= {2012}

}

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