Probabilistic Bisimulations for PCTL Model Checking of Interval MDPs

Verification of PCTL properties of MDPs with convex uncertainties has been investigated recently by Puggelli et al. However, model checking algorithms typically suffer from state space explosion. In this paper, we address probabilistic bisimulation to reduce the size of such an MDPs while preserving PCTL properties it satisfies. We discuss different interpretations of uncertainty in the models which are studied in the literature and that result in two different definitions of bisimulations. We give algorithms to compute the quotients of these bisimulations in time polynomial in the size of the model and exponential in the uncertain branching. Finally, we show by a case study that large models in practice can have small branching and that a substantial state space reduction can be achieved by our approach.Comment: In Proceedings SynCoP 2014, arXiv:1403.784

A Semantical Analysis of Second-Order Propositional Modal Logic

International audienceThis paper is aimed as a contribution to the use of formal modal languages in Artificial Intelligence. We introduce a multi-modal version of Second-order Propositional Modal Logic (SOPML), an extension of modal logic with propositional quantification, and illustrate its usefulness as a specification language for knowledge representation as well as temporal and spatial reasoning. Then, we define novel notions of (bi)simulation and prove that these preserve the interpretation of SOPML formulas. Finally, we apply these results to assess the expressive power of SOPML

A Definition Scheme for Quantitative Bisimulation

FuTS, state-to-function transition systems are generalizations of labeled transition systems and of familiar notions of quantitative semantical models as continuous-time Markov chains, interactive Markov chains, and Markov automata. A general scheme for the definition of a notion of strong bisimulation associated with a FuTS is proposed. It is shown that this notion of bisimulation for a FuTS coincides with the coalgebraic notion of behavioral equivalence associated to the functor on Set given by the type of the FuTS. For a series of concrete quantitative semantical models the notion of bisimulation as reported in the literature is proven to coincide with the notion of quantitative bisimulation obtained from the scheme. The comparison includes models with orthogonal behaviour, like interactive Markov chains, and with multiple levels of behavior, like Markov automata. As a consequence of the general result relating FuTS bisimulation and behavioral equivalence we obtain, in a systematic way, a coalgebraic underpinning of all quantitative bisimulations discussed.Comment: In Proceedings QAPL 2015, arXiv:1509.0816