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Published in:
2012 | OriginalPaper | Chapter
Coalgebraic Trace Semantics for Probabilistic Transition Systems Based on Measure Theory
Authors : Henning Kerstan, Barbara König
Published in: CONCUR 2012 – Concurrency Theory
Publisher: Springer Berlin Heidelberg
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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.