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N. Bertrand, C. Morvan. Probabilistic Regular Graphs. In Infinity, EPTCS, Volume 39, Pages 77-90, Singapore, September 2010.

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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 [8], on probabilistic pushdown automata, using similar methods combined with graph grammars techniques


Nathalie Bertrand http://www.irisa.fr/prive/nbertran/
Christophe Morvan http://www-igm.univ-mlv.fr/~cmorvan/

BibTex Reference

   Author = {Bertrand, N. and Morvan, C.},
   Title = {Probabilistic Regular Graphs},
   BookTitle = {Infinity},
   Volume = {    39},
   Pages = {77--90},
   Series = {EPTCS},
   Address = {Singapore},
   Month = {September},
   Year = {2010}

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