Probabilistic regular graphs

Nathalie Bertrand
(INRIA Rennes Bretagne Atlantique)
Christophe Morvan
(Université Paris-Est and INRIA Rennes Bretagne Atlantique)

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.

In Yu-Fang Chen and Ahmed Rezine: Proceedings 12th International Workshop on Verification of Infinite-State Systems (INFINITY 2010), Singapore, 21st September 2010, Electronic Proceedings in Theoretical Computer Science 39, pp. 77–90.
Published: 28th October 2010.

ArXived at: http://dx.doi.org/10.4204/EPTCS.39.6 bibtex PDF

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