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A Decidable Probability Logic for Timed Probabilistic Systems

Lanotte R., Beauquier D.

Fundamenta Informaticae

2009

Vol. 96, nr 1/2

127-151

In this paper we extend the predicate logic introduced by Beauquier et al. in order to deal with Markov decision processes. We prove that with respect to qualitative probabilistic properties, model checking is decidable for this logic applied to Markov decision processes. Furthermore we apply our logic to probabilistic timed transition systems using predicates on clocks. We prove that results on Markov decision processes hold also for probabilistic timed transition systems. The interest of this logic lies in particular on the fact that some important properties are expressible in this logic but not expressible in pCTL.

Markov Decision Processes and Deterministic Büchi Automata

Beauquier D.

Fundamenta Informaticae

2002

Vol. 50, nr 1

1-13

We prove that given a Markov Decision Process (MDP) and a fixed subset of its states F, there is a Markov policy which maximizes everywhere the probability to reach F infinitely often. Moreover such a maximum policy is computable in polytime in the size of the MDP. This result can be applied in order to control a system with randomized or uncertain behavior with respect to a given property to optimize.