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Efficient Analysis of Probabilistic Programs with an Unbounded Counter

  • Tomáš Brázdil
  • Stefan Kiefer
  • Antonín Kučera
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6806)

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Tomáš Brázdil
    • 1
  • Stefan Kiefer
    • 2
  • Antonín Kučera
    • 1
  1. 1.Faculty of InformaticsMasaryk UniversityCzech Republic
  2. 2.Department of Computer ScienceUniversity of OxfordUnited Kingdom

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