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Algorithmic analysis of qualitative and quantitative termination problems for affine probabilistic programs
, Article ACM SIGPLAN Notices ; Volume 51, Issue 1 , 2016 , Pages 327-342 ; 15232867 (ISSN) ; Fu, H ; Novotný, P ; Hasheminezhad, R ; Sharif University of Technology
Association for Computing Machinery
Abstract
In this paper, we consider termination of probabilistic programs with real-valued variables. The questions concerned are: (a) qualitative ones that ask (i) whether the program terminates with probability 1 (almost-sure termination) and (ii) whether the expected termination time is finite (finite termination); (b) quantitative ones that ask (i) to approximate the expected termination time (expectation problem) and (ii) to compute a bound B such that the probability to terminate after B steps decreases exponentially (concentration problem). To solve these questions, we utilize the notion of ranking supermartingales which is a powerful approach for proving termination of probabilistic programs....
Algorithmic analysis of qualitative and quantitative termination problems for affine probabilistic programs
, Article 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, 20 January 2016 through 22 January 2016 ; Volume 20-22-January-2016 , 2016 , Pages 327-342 ; 07308566 (ISSN) ; 9781450335492 (ISBN) ; Fu, H ; Novotný, P ; Hasheminezhad, R ; Majumdar, R ; Bodik, R ; Association for Computing Machinery (ACM) SIGPLAN ; Sharif University of Technology
Association for Computing Machinery
Abstract
In this paper, we consider termination of probabilistic programs with real-valued variables. The questions concerned are: (a) qualitative ones that ask (i) whether the program terminates with probability 1 (almost-sure termination) and (ii) whether the expected termination time is finite (finite termination); (b) quantitative ones that ask (i) to approximate the expected termination time (expectation problem) and (ii) to compute a bound B such that the probability to terminate after B steps decreases exponentially (concentration problem). To solve these questions, we utilize the notion of ranking supermartingales which is a powerful approach for proving termination of probabilistic programs....