On Lexicographic Proof Rules for Probabilistic Termination
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.
Cite
@article{arxiv.2108.02188,
title = {On Lexicographic Proof Rules for Probabilistic Termination},
author = {Krishnendu Chatterjee and Ehsan Kafshdar Goharshady and Petr Novotný and Jiří Zárevúcky and Đorđe Žikelić},
journal= {arXiv preprint arXiv:2108.02188},
year = {2021}
}