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.
24th International Symposium on Formal Methods
This research was partially supported by the ERC CoG 863818 (ForM-SMArt), the Czech Science Foundation grant No. GJ19-15134Y, and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385.
FM: Formal Methods
2021-11-20 – 2021-11-26
Chatterjee K, Goharshady EK, Novotný P, Zárevúcky J, Žikelić Đ. On lexicographic proof rules for probabilistic termination. In: 24th International Symposium on Formal Methods. Vol 13047. Springer Nature; 2021:619-639. doi:10.1007/978-3-030-90870-6_33
Chatterjee, K., Goharshady, E. K., Novotný, P., Zárevúcky, J., & Žikelić, Đ. (2021). On lexicographic proof rules for probabilistic termination. In 24th International Symposium on Formal Methods (Vol. 13047, pp. 619–639). Virtual: Springer Nature. https://doi.org/10.1007/978-3-030-90870-6_33
Chatterjee, Krishnendu, Ehsan Kafshdar Goharshady, Petr Novotný, Jiří Zárevúcky, and Đorđe Žikelić. “On Lexicographic Proof Rules for Probabilistic Termination.” In 24th International Symposium on Formal Methods, 13047:619–39. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-90870-6_33.
K. Chatterjee, E. K. Goharshady, P. Novotný, J. Zárevúcky, and Đ. Žikelić, “On lexicographic proof rules for probabilistic termination,” in 24th International Symposium on Formal Methods, Virtual, 2021, vol. 13047, pp. 619–639.
Chatterjee K, Goharshady EK, Novotný P, Zárevúcky J, Žikelić Đ. 2021. On lexicographic proof rules for probabilistic termination. 24th International Symposium on Formal Methods. FM: Formal Methods, LNCS, vol. 13047, 619–639.
Chatterjee, Krishnendu, et al. “On Lexicographic Proof Rules for Probabilistic Termination.” 24th International Symposium on Formal Methods, vol. 13047, Springer Nature, 2021, pp. 619–39, doi:10.1007/978-3-030-90870-6_33.