@article{14778,
  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.},
  author       = {Chatterjee, Krishnendu and Kafshdar Goharshady, Ehsan and Novotný, Petr and Zárevúcky, Jiří and Zikelic, Dorde},
  issn         = {1433-299X},
  journal      = {Formal Aspects of Computing},
  keywords     = {Theoretical Computer Science, Software},
  number       = {2},
  publisher    = {Association for Computing Machinery},
  title        = {{On lexicographic proof rules for probabilistic termination}},
  doi          = {10.1145/3585391},
  volume       = {35},
  year         = {2023},
}