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arXiv · 2108.02188

On Lexicographic Proof Rules for Probabilistic Termination

Krishnendu Chatterjee·Ehsan Kafshdar Goharshady·Petr Novotný·Jiří Zárevúcky·Đorđe Žikelić
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Abstract

We consider the almost-sure (a.s.) termination problem for probabilistic programs, which are a stochastic extension of classical imperative programs. Lexicographic ranking functions provide a sound and practical approach for termination of non-probabilistic programs, and their extension to probabilistic programs is achieved via lexicographic ranking supermartingales (LexRSMs). However, LexRSMs introduced in the previous work have a limitation that impedes their automation: all of their components have to be non-negative in all reachable states. This might result in LexRSM not existing even for simple terminating programs. Our contributions are twofold: First, we introduce a generalization of LexRSMs which allows for some components to be negative. This standard feature of non-probabilistic termination proofs was hitherto not known to be sound in the probabilistic setting, as the soundness proof requires a careful analysis of the underlying stochastic process. Second, we present polynomial-time algorithms using our generalized LexRSMs for proving a.s. termination in broad classes of linear-arithmetic programs.

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Krishnendu Chatterjee, Ehsan Kafshdar Goharshady, Petr Novotný, Jiří Zárevúcky, Đorđe Žikelić. 2021-08-04. On Lexicographic Proof Rules for Probabilistic Termination. https://arxiv.org/abs/2108.02188

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