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arXiv · 1805.10749

Ranking and Repulsing Supermartingales for Reachability in Probabilistic Programs

Toru Takisaka·Yuichiro Oyabu·Natsuki Urabe·Ichiro Hasuo
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Abstract

Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating reachability probabilities. Based on the existing works that stretch across different communities (formal verification, control theory, etc.), we offer a unifying account. In particular, we emphasize the role of order-theoretic fixed points---a classic topic in computer science---in the analysis of probabilistic programs. This leads us to two new martingale-based techniques, too. We give rigorous proofs for their soundness and completeness. We also make an experimental comparison using our implementation of template-based synthesis algorithms for those martingales.

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Toru Takisaka, Yuichiro Oyabu, Natsuki Urabe, Ichiro Hasuo. 2018-05-28. Ranking and Repulsing Supermartingales for Reachability in Probabilistic Programs. https://doi.org/10.1007/978-3-030-01090-4_28

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