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Modular verification for almost-sure termination of probabilistic programs

Authors:

Mingzhang Huang,

Krishnendu Chatterjee,

Amir Kafshdar GoharshadyAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 3, Issue OOPSLA

Article No.: 129, Pages 1 - 29

https://doi.org/10.1145/3360555

Published: 10 October 2019 Publication History

Abstract

In this work, we consider the almost-sure termination problem for probabilistic programs that asks whether a given probabilistic program terminates with probability 1. Scalable approaches for program analysis often rely on modularity as their theoretical basis. In non-probabilistic programs, the classical variant rule (V-rule) of Floyd-Hoare logic provides the foundation for modular analysis. Extension of this rule to almost-sure termination of probabilistic programs is quite tricky, and a probabilistic variant was proposed by Fioriti and Hermanns in POPL 2015. While the proposed probabilistic variant cautiously addresses the key issue of integrability, we show that the proposed modular rule is still not sound for almost-sure termination of probabilistic programs.

Besides establishing unsoundness of the previous rule, our contributions are as follows: First, we present a sound modular rule for almost-sure termination of probabilistic programs. Our approach is based on a novel notion of descent supermartingales. Second, for algorithmic approaches, we consider descent supermartingales that are linear and show that they can be synthesized in polynomial time. Finally, we present experimental results on a variety of benchmarks and several natural examples that model various types of nested while loops in probabilistic programs and demonstrate that our approach is able to efficiently prove their almost-sure termination property.

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Chatterjee KGoharshady AMeggendorfer TŽikelić Đ(2024)Quantitative Bounds on Resource Usage of Probabilistic ProgramsProceedings of the ACM on Programming Languages10.1145/36498248:OOPSLA1(362-391)Online publication date: 29-Apr-2024
https://dl.acm.org/doi/10.1145/3649824
Kassing JDollase SGiesl J(2024)A Complete Dependency Pair Framework for Almost-Sure Innermost Termination of Probabilistic Term RewritingFunctional and Logic Programming10.1007/978-981-97-2300-3_4(62-80)Online publication date: 15-May-2024
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Takisaka TZhang LWang CLiu J(2024)Lexicographic Ranking Supermartingales with Lazy Lower BoundsComputer Aided Verification10.1007/978-3-031-65633-0_19(420-442)Online publication date: 26-Jul-2024
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Index Terms

Modular verification for almost-sure termination of probabilistic programs
1. Theory of computation
  1. Logic
    1. Automated reasoning
    2. Logic and verification
  2. Semantics and reasoning
    1. Program reasoning
      1. Program verification

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 3, Issue OOPSLA

October 2019

2077 pages

EISSN:2475-1421

DOI:10.1145/3366395

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Copyright © 2019 Owner/Author.

This work is licensed under a Creative Commons Attribution-NoDerivs International 4.0 License.

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Association for Computing Machinery

New York, NY, United States

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Published: 10 October 2019

Published in PACMPL Volume 3, Issue OOPSLA

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National Natural Science Foundation of China
European Research Council
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Vienna Science and Technology Fund
Shanghai Key Laboratory of Trustworthy Computing
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Österreichischen Akademie der Wissenschaften

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Cited By

Chatterjee KGoharshady AMeggendorfer TŽikelić Đ(2024)Quantitative Bounds on Resource Usage of Probabilistic ProgramsProceedings of the ACM on Programming Languages10.1145/36498248:OOPSLA1(362-391)Online publication date: 29-Apr-2024
https://dl.acm.org/doi/10.1145/3649824
Kassing JDollase SGiesl J(2024)A Complete Dependency Pair Framework for Almost-Sure Innermost Termination of Probabilistic Term RewritingFunctional and Logic Programming10.1007/978-981-97-2300-3_4(62-80)Online publication date: 15-May-2024
https://dl.acm.org/doi/10.1007/978-981-97-2300-3_4
Takisaka TZhang LWang CLiu J(2024)Lexicographic Ranking Supermartingales with Lazy Lower BoundsComputer Aided Verification10.1007/978-3-031-65633-0_19(420-442)Online publication date: 26-Jul-2024
https://doi.org/10.1007/978-3-031-65633-0_19
Kassing JFrohn FGiesl J(2024)From Innermost to Full Almost-Sure Termination of Probabilistic Term RewritingFoundations of Software Science and Computation Structures10.1007/978-3-031-57231-9_10(206-228)Online publication date: 6-Apr-2024
https://dl.acm.org/doi/10.1007/978-3-031-57231-9_10
Cai ZFarokhnia SGoharshady AHitarth S(2023)Asparagus: Automated Synthesis of Parametric Gas Upper-Bounds for Smart ContractsProceedings of the ACM on Programming Languages10.1145/36228297:OOPSLA2(882-911)Online publication date: 16-Oct-2023
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Chatterjee KKafshdar Goharshady ENovotný PZárevúcky JŽikelić Đ(2023)On Lexicographic Proof Rules for Probabilistic TerminationFormal Aspects of Computing10.1145/358539135:2(1-25)Online publication date: 23-Jun-2023
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Kassing JGiesl J(2023)Proving Almost-Sure Innermost Termination of Probabilistic Term Rewriting Using Dependency PairsAutomated Deduction – CADE 2910.1007/978-3-031-38499-8_20(344-364)Online publication date: 1-Jul-2023
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de Amorim P(2023)A Higher-Order Language for Markov Kernels and Linear OperatorsFoundations of Software Science and Computation Structures10.1007/978-3-031-30829-1_5(89-112)Online publication date: 21-Apr-2023
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