Automated Termination Analysis of Polynomial Probabilistic Programs

Abstract The termination behavior of probabilistic programs depends on the outcomes random assignments. Almost sure (AST) is concerned with question whether a program terminates probability one all possible inputs. Positive almost (PAST) focuses in finite expected number steps. This paper presents fully automated approach to analysis while-programs whose guards and expressions are polynomial expressions. As proving (positive) AST undecidable general, existing proof rules typically provide sufficient conditions. These conditions mostly involve constraints supermartingales. We consider four from literature extend these generalizations for (P)AST. automate resulting set by effectively computing asymptotic bounds polynomials over variables. used decide – including supermartingales rule. Our software tool Amber can thus check AST, PAST, as well their negations large class programs, while carrying out reasoning witnesses. Experimental results show merits our generalized demonstrate that handle reach other state-of-the-art tools.