--- res: bibo_abstract: - 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.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Krishnendu foaf_name: Chatterjee, Krishnendu foaf_surname: Chatterjee foaf_workInfoHomepage: http://www.librecat.org/personId=2E5DCA20-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-4561-241X - foaf_Person: foaf_givenName: Hongfei foaf_name: Fu, Hongfei foaf_surname: Fu foaf_workInfoHomepage: http://www.librecat.org/personId=3AAD03D6-F248-11E8-B48F-1D18A9856A87 - foaf_Person: foaf_givenName: Amir foaf_name: Goharshady, Amir foaf_surname: Goharshady foaf_workInfoHomepage: http://www.librecat.org/personId=391365CE-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0003-1702-6584 bibo_doi: 10.1007/978-3-319-41528-4_1 bibo_volume: 9779 dct_date: 2016^xs_gYear dct_language: eng dct_publisher: Springer@ dct_title: Termination analysis of probabilistic programs through Positivstellensatz's@ ...