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@inproceedings{1797365,
author = {Chatterjee, Krishnendu and Goharshady, Ehsan Kafshdar and Novotný, Petr and Zárevúcky, Jiří and Žikelić, Djordje},
address = {Cham, Switzerland},
booktitle = {24th International Symposium on Formal Methods, FM 2021},
doi = {http://dx.doi.org/10.1007/978-3-030-90870-6_33},
keywords = {program analysis; probabilistic programs; almost-sure termination; martingales},
howpublished = {elektronická verze "online"},
language = {eng},
location = {Cham, Switzerland},
isbn = {978-3-030-90869-0},
pages = {619-639},
publisher = {Springer},
title = {On Lexicographic Proof Rules for Probabilistic Termination},
year = {2021}
}
TY - JOUR
ID - 1797365
AU - Chatterjee, Krishnendu - Goharshady, Ehsan Kafshdar - Novotný, Petr - Zárevúcky, Jiří - Žikelić, Djordje
PY - 2021
TI - On Lexicographic Proof Rules for Probabilistic Termination
PB - Springer
CY - Cham, Switzerland
SN - 9783030908690
KW - program analysis
KW - probabilistic programs
KW - almost-sure termination
KW - martingales
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 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.
ER -
CHATTERJEE, Krishnendu, Ehsan Kafshdar GOHARSHADY, Petr NOVOTNÝ, Jiří ZÁREVÚCKY and Djordje ŽIKELI$\backslash$'C. On Lexicographic Proof Rules for Probabilistic Termination. Online. In \textit{24th International Symposium on Formal Methods, FM 2021}. Cham, Switzerland: Springer, 2021, p.~619-639. ISBN~978-3-030-90869-0. Available from: https://dx.doi.org/10.1007/978-3-030-90870-6\_{}33.
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