@inproceedings{10414,
  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.},
  author       = {Chatterjee, Krishnendu and Goharshady, Ehsan Kafshdar and Novotný, Petr and Zárevúcky, Jiří and Zikelic, Dorde},
  booktitle    = {24th International Symposium on Formal Methods},
  isbn         = {9-783-0309-0869-0},
  issn         = {1611-3349},
  location     = {Virtual},
  pages        = {619--639},
  publisher    = {Springer Nature},
  title        = {{On lexicographic proof rules for probabilistic termination}},
  doi          = {10.1007/978-3-030-90870-6_33},
  volume       = {13047},
  year         = {2021},
}