| CHATTERJEE, Krishnendu, Ehsan Kafshdar GOHARSHADY, Petr NOVOTNÝ, Jiří ZÁREVÚCKY and Djordje ŽIKELIĆ. On Lexicographic Proof Rules for Probabilistic Termination. Formal Aspects of Computing. 2023, vol. 35, No 2, p. "11:1"-"11:25", 25 pp. ISSN 0934-5043. Available from: https://dx.doi.org/10.1145/3585391. |
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@article{2386721,
author = {Chatterjee, Krishnendu and Goharshady, Ehsan Kafshdar and Novotný, Petr and Zárevúcky, Jiří and Žikelić, Djordje},
article_number = {2},
doi = {http://dx.doi.org/10.1145/3585391},
keywords = {probabilistic programs; termination; martingales},
language = {eng},
issn = {0934-5043},
journal = {Formal Aspects of Computing},
title = {On Lexicographic Proof Rules for Probabilistic Termination},
url = {https://dl.acm.org/doi/10.1145/3585391},
volume = {35},
year = {2023}
}
TY - JOUR
ID - 2386721
AU - Chatterjee, Krishnendu - Goharshady, Ehsan Kafshdar - Novotný, Petr - Zárevúcky, Jiří - Žikelić, Djordje
PY - 2023
TI - On Lexicographic Proof Rules for Probabilistic Termination
JF - Formal Aspects of Computing
VL - 35
IS - 2
SP - "11:1"-"11:25"
EP - "11:1"-"11:25"
SN - 09345043
KW - probabilistic programs
KW - termination
KW - martingales
UR - https://dl.acm.org/doi/10.1145/3585391
N2 - 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.
ER -
CHATTERJEE, Krishnendu, Ehsan Kafshdar GOHARSHADY, Petr NOVOTNÝ, Jiří ZÁREVÚCKY and Djordje ŽIKELI$\backslash$'C. On Lexicographic Proof Rules for Probabilistic Termination. \textit{Formal Aspects of Computing}. 2023, vol.~35, No~2, p.~''11:1''-''11:25'', 25 pp. ISSN~0934-5043. Available from: https://dx.doi.org/10.1145/3585391.
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