eprintid: 10089705 rev_number: 18 eprint_status: archive userid: 608 dir: disk0/10/08/97/05 datestamp: 2020-01-29 16:41:59 lastmod: 2021-10-19 22:21:42 status_changed: 2020-01-29 16:41:59 type: proceedings_section metadata_visibility: show creators_name: McIver, A creators_name: Morgan, C creators_name: Kaminski, BL creators_name: Katoen, J-P title: A New Proof Rule for Almost-Sure Termination ispublished: pub divisions: UCL divisions: B04 divisions: C05 divisions: F48 keywords: cs.PL, cs.PL, cs.LO note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. abstract: An important question for a probabilistic program is whether the probability mass of all its diverging runs is zero, that is that it terminates "almost surely". Proving that can be hard, and this paper presents a new method for doing so; it is expressed in a program logic, and so applies directly to source code. The programs may contain both probabilistic- and demonic choice, and the probabilistic choices may depend on the current state. As do other researchers, we use variant functions (a.k.a. "super-martingales") that are real-valued and probabilistically might decrease on each loop iteration; but our key innovation is that the amount as well as the probability of the decrease are parametric. We prove the soundness of the new rule, indicate where its applicability goes beyond existing rules, and explain its connection to classical results on denumerable (non-demonic) Markov chains. date: 2018-01 publisher: ACM official_url: https://doi.org/10.1145/3158121 oa_status: green full_text_type: other language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 1741702 doi: 10.1145/3158121 lyricists_name: Kaminski, Benjamin lyricists_id: BKAMI07 actors_name: Kaminski, Benjamin actors_id: BKAMI07 actors_role: owner full_text_status: public volume: 2 place_of_pub: Los Angeles, California, USA pagerange: 33 event_title: 45th ACM SIGPLAN Symposium on Principles of Programming Languages (POPL 2018) book_title: Proceedings of the ACM on Programming Languages citation: McIver, A; Morgan, C; Kaminski, BL; Katoen, J-P; (2018) A New Proof Rule for Almost-Sure Termination. In: Proceedings of the ACM on Programming Languages. (pp. p. 33). ACM: Los Angeles, California, USA. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10089705/1/1711.03588v2.pdf