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ENTCS
2007

Labelled Markov Processes as Generalised Stochastic Relations

13 years 3 months ago
Labelled Markov Processes as Generalised Stochastic Relations
Labelled Markov processes (LMPs) are labelled transition systems in which each transition has an associated probability. In this paper we present a universal LMP as the spectrum of a commutative C∗-algebra consisting of formal linear combinations of labelled trees. This yields a simple trace-tree semantics for LMPs that is fully with respect to probabilistic bisimilarity. We also consider LMPs with distinguished entry and exit points as stateful stochastic relations. This allows us to define a category LMP, with measurable spaces as objects and LMPs as morphisms. Our main result in this context is to provide a predicate-transformer duality for LMP that generalises Kozen’s duality for the category SRel of stochastic relations. Key words: Labelled Markov process, Stochastic relation, Probabilistic bisimulation, Stone duality, C∗-algebra, Comonad.
Michael W. Mislove, Dusko Pavlovic, James Worrell
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2007
Where ENTCS
Authors Michael W. Mislove, Dusko Pavlovic, James Worrell
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