Article

Proving termination of probabilistic programs using patterns

Authors:

Javier Esparza,

Andreas Gaiser,

Stefan KieferAuthors Info & Claims

CAV'12: Proceedings of the 24th international conference on Computer Aided Verification

Pages 123 - 138

https://doi.org/10.1007/978-3-642-31424-7_14

Published: 07 July 2012 Publication History

Abstract

Proving programs terminating is a fundamental computer science challenge. Recent research has produced powerful tools that can check a wide range of programs for termination. The analog for probabilistic programs, namely termination with probability one ("almost-sure termination"), is an equally important property for randomized algorithms and probabilistic protocols. We suggest a novel algorithm for proving almost-sure termination of probabilistic programs. Our algorithm exploits the power of state-of-the-art model checkers and termination provers for nonprobabilistic programs: it calls such tools within a refinement loop and thereby iteratively constructs a "terminating pattern", which is a set of terminating runs with probability one. We report on various case studies illustrating the effectiveness of our algorithm. As a further application, our algorithm can improve lower bounds on reachability probabilities.

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Cited By

Gregersen SAguirre AHaselwarter PTassarotti JBirkedal L(2024)Almost-Sure Termination by Guarded RefinementProceedings of the ACM on Programming Languages10.1145/36746328:ICFP(203-233)Online publication date: 15-Aug-2024
https://dl.acm.org/doi/10.1145/3674632
Yu N(2023)Structured Theorem for Quantum Programs and its ApplicationsACM Transactions on Software Engineering and Methodology10.1145/358715432:4(1-35)Online publication date: 26-May-2023
https://dl.acm.org/doi/10.1145/3587154
Moosbrugger MBartocci EKatoen JKovács L(2022)The probabilistic termination tool amberFormal Methods in System Design10.1007/s10703-023-00424-z61:1(90-109)Online publication date: 1-Aug-2022
https://dl.acm.org/doi/10.1007/s10703-023-00424-z
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Published In

cover image Guide Proceedings

CAV'12: Proceedings of the 24th international conference on Computer Aided Verification

July 2012

789 pages

ISBN:9783642314230

Editors:
P. Madhusudan
Dept. of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL
,
Sanjit A. Seshia
Dept. of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA

Sponsors

NEC Labs: NEC Labs
IBMR: IBM Research
Intel: Intel
Microsoft Research: Microsoft Research

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Springer-Verlag

Berlin, Heidelberg

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Published: 07 July 2012

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Cited By

Gregersen SAguirre AHaselwarter PTassarotti JBirkedal L(2024)Almost-Sure Termination by Guarded RefinementProceedings of the ACM on Programming Languages10.1145/36746328:ICFP(203-233)Online publication date: 15-Aug-2024
https://dl.acm.org/doi/10.1145/3674632
Yu N(2023)Structured Theorem for Quantum Programs and its ApplicationsACM Transactions on Software Engineering and Methodology10.1145/358715432:4(1-35)Online publication date: 26-May-2023
https://dl.acm.org/doi/10.1145/3587154
Moosbrugger MBartocci EKatoen JKovács L(2022)The probabilistic termination tool amberFormal Methods in System Design10.1007/s10703-023-00424-z61:1(90-109)Online publication date: 1-Aug-2022
https://dl.acm.org/doi/10.1007/s10703-023-00424-z
Wang JSun YFu HChatterjee KGoharshady AFreund SYahav E(2021)Quantitative analysis of assertion violations in probabilistic programsProceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation10.1145/3453483.3454102(1171-1186)Online publication date: 19-Jun-2021
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Moosbrugger MBartocci EKatoen JKovács L(2021)The Probabilistic Termination Tool AmberFormal Methods10.1007/978-3-030-90870-6_36(667-675)Online publication date: 20-Nov-2021
https://dl.acm.org/doi/10.1007/978-3-030-90870-6_36
Esparza J(2021)Population Protocols: Beyond Runtime AnalysisReachability Problems10.1007/978-3-030-89716-1_3(28-51)Online publication date: 25-Oct-2021
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Chen JHe FDonaldson ATorlak E(2020)Proving almost-sure termination by omega-regular decompositionProceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation10.1145/3385412.3386002(869-882)Online publication date: 11-Jun-2020
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Avanzini MLago UGhyselen ABouyer P(2019)Type-based complexity analysis of probabilistic functional programsProceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3470152.3470193(1-13)Online publication date: 24-Jun-2019
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Kobayashi NLago UGrellois CBouyer P(2019)On the termination problem for probabilistic higher-order recursive programsProceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3470152.3470177(1-14)Online publication date: 24-Jun-2019
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Wang PFu HGoharshady AChatterjee KQin XShi WMcKinley KFisher K(2019)Cost analysis of nondeterministic probabilistic programsProceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation10.1145/3314221.3314581(204-220)Online publication date: 8-Jun-2019
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