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Runtime analysis of probabilistic programs with unbounded recursion

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BRÁZDIL Tomáš KIEFER Stefan KUČERA Antonín HUTAŘOVÁ VAŘEKOVÁ Ivana

Druh Článek v odborném periodiku
Časopis / Zdroj Journal of Computer and System Sciences
Fakulta / Pracoviště MU

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Citace
Doi http://dx.doi.org/10.1016/j.jcss.2014.06.005
Obor Informatika
Klíčová slova pushdown automata; recursion
Popis We study the runtime in probabilistic programs with unbounded recursion. As underlying formal model for such programs we use probabilistic pushdown automata (pPDAs) which exactly correspond to recursive Markov chains. We show that every pPDA can be transformed into a stateless pPDA (called "pBPA") whose runtime and further properties are closely related to those of the original pPDA. This result substantially simplifies the analysis of runtime and other pPDA properties. We prove that for every pPDA the probability of performing a long run decreases exponentially in the length of the run, if and only if the expected runtime in the pPDA is finite. If the expectation is infinite, then the probability decreases "polynomially". We show that these bounds are asymptotically tight. Our tail bounds on the runtime are generic, i.e., applicable to any probabilistic program with unbounded recursion.
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