On lexicographic proof rules for probabilistic termination
Chatterjee K, Kafshdar Goharshady E, Novotný P, Zárevúcky J, Zikelic D. 2023. On lexicographic proof rules for probabilistic termination. Formal Aspects of Computing. 35(2), 11.
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Chatterjee, KrishnenduISTA ;
Kafshdar Goharshady, Ehsan;
Novotny, PetrISTA;
Zárevúcky, Jiří;
Zikelic, DjordjeISTA
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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 a LexRSM not existing even for simple terminating programs. Our contributions are twofold. First, we introduce a generalization of LexRSMs that 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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Date Published
2023-06-23
Journal Title
Formal Aspects of Computing
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Association for Computing Machinery
Acknowledgement
This research was partially supported by the ERC CoG (grant no. 863818; ForM-SMArt), the Czech Science Foundation (grant no. GA21-24711S), and the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 665385.
Volume
35
Issue
2
Article Number
11
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Cite this
Chatterjee K, Kafshdar Goharshady E, Novotný P, Zárevúcky J, Zikelic D. On lexicographic proof rules for probabilistic termination. Formal Aspects of Computing. 2023;35(2). doi:10.1145/3585391
Chatterjee, K., Kafshdar Goharshady, E., Novotný, P., Zárevúcky, J., & Zikelic, D. (2023). On lexicographic proof rules for probabilistic termination. Formal Aspects of Computing. Association for Computing Machinery. https://doi.org/10.1145/3585391
Chatterjee, Krishnendu, Ehsan Kafshdar Goharshady, Petr Novotný, Jiří Zárevúcky, and Dorde Zikelic. “On Lexicographic Proof Rules for Probabilistic Termination.” Formal Aspects of Computing. Association for Computing Machinery, 2023. https://doi.org/10.1145/3585391.
K. Chatterjee, E. Kafshdar Goharshady, P. Novotný, J. Zárevúcky, and D. Zikelic, “On lexicographic proof rules for probabilistic termination,” Formal Aspects of Computing, vol. 35, no. 2. Association for Computing Machinery, 2023.
Chatterjee K, Kafshdar Goharshady E, Novotný P, Zárevúcky J, Zikelic D. 2023. On lexicographic proof rules for probabilistic termination. Formal Aspects of Computing. 35(2), 11.
Chatterjee, Krishnendu, et al. “On Lexicographic Proof Rules for Probabilistic Termination.” Formal Aspects of Computing, vol. 35, no. 2, 11, Association for Computing Machinery, 2023, doi:10.1145/3585391.
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