Probabilistic Regular Graphs

Nathalie Bertrand (1) , Christophe Morvan (1)

1 VERTECS - Verification models and techniques applied to testing and control of reactive systems

Deterministic graph grammars generate regular graphs, that form a structural extension of configuration graphs of pushdown systems. In this paper, we study a probabilistic extension of regular graphs obtained by labelling the terminal arcs of the graph grammars by probabilities. Stochastic properties of these graphs are expressed using PCTL, a probabilistic extension of computation tree logic. We present here an algorithm to perform approximate verification of PCTL formulae. Moreover, we prove that the exact model-checking problem for PCTL on probabilistic regular graphs is undecidable, unless restricting to qualitative properties. Our results generalise those of [EKM06], on probabilistic pushdown automata, using similar methods combined with graph grammars techniques.

Domaines: Mathématique discrète [cs.DM]

Nathalie Bertrand, Christophe Morvan. Probabilistic Regular Graphs. Infinity (International Workshop on Verification of Infinite-State Systems), 2010, Singapour, Singapore. pp.77-90. ⟨inria-00525388⟩