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arXiv · 1601.01001

Weakest Precondition Reasoning for Expected Run-Times of Probabilistic Programs

Benjamin Lucien Kaminski·Joost-Pieter Katoen·Christoph Matheja·Federico Olmedo
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Abstract

This paper presents a wp-style calculus for obtaining bounds on the expected run-time of probabilistic programs. Its application includes determining the (possibly infinite) expected termination time of a probabilistic program and proving positive almost-sure termination - does a program terminate with probability one in finite expected time? We provide several proof rules for bounding the run-time of loops, and prove the soundness of the approach with respect to a simple operational model. We show that our approach is a conservative extension of Nielson's approach for reasoning about the run-time of deterministic programs. We analyze the expected run-time of some example programs including a one-dimensional random walk and the coupon collector problem.

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Benjamin Lucien Kaminski, Joost-Pieter Katoen, Christoph Matheja, Federico Olmedo. 2016-01-05. Weakest Precondition Reasoning for Expected Run-Times of Probabilistic Programs. https://arxiv.org/abs/1601.01001

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