--- _id: '1386' abstract: - lang: eng text: We consider nondeterministic probabilistic programs with the most basic liveness property of termination. We present efficient methods for termination analysis of nondeterministic probabilistic programs with polynomial guards and assignments. Our approach is through synthesis of polynomial ranking supermartingales, that on one hand significantly generalizes linear ranking supermartingales and on the other hand is a counterpart of polynomial ranking-functions for proving termination of nonprobabilistic programs. The approach synthesizes polynomial ranking-supermartingales through Positivstellensatz's, yielding an efficient method which is not only sound, but also semi-complete over a large subclass of programs. We show experimental results to demonstrate that our approach can handle several classical programs with complex polynomial guards and assignments, and can synthesize efficient quadratic ranking-supermartingales when a linear one does not exist even for simple affine programs. alternative_title: - LNCS author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Hongfei full_name: Fu, Hongfei id: 3AAD03D6-F248-11E8-B48F-1D18A9856A87 last_name: Fu - first_name: Amir full_name: Goharshady, Amir id: 391365CE-F248-11E8-B48F-1D18A9856A87 last_name: Goharshady orcid: 0000-0003-1702-6584 citation: ama: 'Chatterjee K, Fu H, Goharshady AK. Termination analysis of probabilistic programs through Positivstellensatz’s. In: Vol 9779. Springer; 2016:3-22. doi:10.1007/978-3-319-41528-4_1' apa: 'Chatterjee, K., Fu, H., & Goharshady, A. K. (2016). Termination analysis of probabilistic programs through Positivstellensatz’s (Vol. 9779, pp. 3–22). Presented at the CAV: Computer Aided Verification, Toronto, Canada: Springer. https://doi.org/10.1007/978-3-319-41528-4_1' chicago: Chatterjee, Krishnendu, Hongfei Fu, and Amir Kafshdar Goharshady. “Termination Analysis of Probabilistic Programs through Positivstellensatz’s,” 9779:3–22. Springer, 2016. https://doi.org/10.1007/978-3-319-41528-4_1. ieee: 'K. Chatterjee, H. Fu, and A. K. Goharshady, “Termination analysis of probabilistic programs through Positivstellensatz’s,” presented at the CAV: Computer Aided Verification, Toronto, Canada, 2016, vol. 9779, pp. 3–22.' ista: 'Chatterjee K, Fu H, Goharshady AK. 2016. Termination analysis of probabilistic programs through Positivstellensatz’s. CAV: Computer Aided Verification, LNCS, vol. 9779, 3–22.' mla: Chatterjee, Krishnendu, et al. Termination Analysis of Probabilistic Programs through Positivstellensatz’s. Vol. 9779, Springer, 2016, pp. 3–22, doi:10.1007/978-3-319-41528-4_1. short: K. Chatterjee, H. Fu, A.K. Goharshady, in:, Springer, 2016, pp. 3–22. conference: end_date: 2016-07-23 location: Toronto, Canada name: 'CAV: Computer Aided Verification' start_date: 2016-07-17 date_created: 2018-12-11T11:51:43Z date_published: 2016-07-01T00:00:00Z date_updated: 2024-03-18T23:30:34Z day: '01' department: - _id: KrCh doi: 10.1007/978-3-319-41528-4_1 ec_funded: 1 intvolume: ' 9779' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1604.07169 month: '07' oa: 1 oa_version: Preprint page: 3 - 22 project: - _id: 25832EC2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S 11407_N23 name: Rigorous Systems Engineering - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 25EE3708-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '267989' name: Quantitative Reactive Modeling publication_status: published publisher: Springer publist_id: '5824' quality_controlled: '1' related_material: record: - id: '8934' relation: dissertation_contains status: public scopus_import: 1 status: public title: Termination analysis of probabilistic programs through Positivstellensatz's type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 9779 year: '2016' ...