Efficient analysis of probabilistic programs with an unbounded counter

Authors:
Tomáš Brázdil;Stefan Kiefer;Antonín Kučera
Affiliations:
Faculty of Informatics, Masaryk University, Czech Republic;Department of Computer Science, University of Oxford, United Kingdom;Faculty of Informatics, Masaryk University, Czech Republic
Venue:
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Year:
2011

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Abstract

We show that a subclass of infinite-state probabilistic programs that can be modeled by probabilistic one-counter automata (pOC) admits an efficient quantitative analysis. In particular, we show that the expected termination time can be approximated up to an arbitrarily small relative error with polynomially many arithmetic operations, and the same holds for the probability of all runs that satisfy a given ω-regular property. Further, our results establish a powerful link between pOC and martingale theory, which leads to fundamental observations about quantitative properties of runs in pOC. In particular, we provide a "divergence gap theorem", which bounds a positive non-termination probability in pOC away from zero.