Kerstan, Henning; König, Barbara:
Coalgebraic Trace Semantics for Probabilistic Transition Systems based on Measure Theory
Duisburg: DuEPublico, 2012
(Technische Berichte der Abteilung für Informatik und Angewandte Kognitionswissenschaft ; 2012-02)
2012BuchOA Gold
InformatikFakultät für Ingenieurwissenschaften » Informatik und Angewandte Kognitionswissenschaft
Titel in Englisch:
Coalgebraic Trace Semantics for Probabilistic Transition Systems based on Measure Theory
Autor*in:
Kerstan, HenningUDE
LSF ID
53779
Sonstiges
der Hochschule zugeordnete*r Autor*in
;
König, BarbaraUDE
GND
1050396502
LSF ID
15982
ORCID
0000-0002-4193-2889ORCID iD
Sonstiges
der Hochschule zugeordnete*r Autor*in
Erscheinungsort:
Duisburg
Verlag:
DuEPublico
Erscheinungsjahr:
2012
Open Access?:
OA Gold
DuEPublico 1 ID
Notiz:
OA gold
Sprache des Textes:
Englisch

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.