Reference:

Tomáš Brázdil, Stefan Kiefer, and Antonín Kučera. Efficient analysis of probabilistic programs with an unbounded counter. Journal of the ACM, 61(6):41:1–41:35, December 2014.

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. We start by establishing 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. Using these observations, we show that the expected termination time can be approximated up to an arbitrarily small relative error in polynomial time, and the same holds for the probability of all runs that satisfy a given omega-regular property encoded by a deterministic Rabin automaton.

Suggested BibTeX entry:

@article{14JACM-BKK,
    author = {Tom\'{a}\v{s} Br\'{a}zdil and Stefan Kiefer and Anton\'{\i}n Ku\v{c}era},
    journal = {Journal of the ACM},
    month = {December},
    number = {6},
    pages = {41:1--41:35},
    publisher = {ACM},
    title = {Efficient Analysis of Probabilistic Programs with an Unbounded Counter},
    volume = {61},
    year = {2014}
}