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Ranking and Repulsing Supermartingales for Reachability in Randomized Programs

Authors:

Yuichiro Oyabu,

Ichiro HasuoAuthors Info & Claims

ACM Transactions on Programming Languages and Systems (TOPLAS), Volume 43, Issue 2

Article No.: 5, Pages 1 - 46

https://doi.org/10.1145/3450967

Published: 08 June 2021 Publication History

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Abstract

Computing reachability probabilities is a fundamental problem in the analysis of randomized programs. This article aims at a comprehensive and comparative account of various martingale-based methods for over- and under-approximating reachability probabilities. Based on the existing works that stretch across different communities (formal verification, control theory, etc.), we offer a unifying account. In particular, we emphasize the role of order-theoretic fixed points—a classic topic in computer science—in the analysis of randomized programs. This leads us to two new martingale-based techniques, too. We also make an experimental comparison using our implementation of template-based synthesis algorithms for those martingales.

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Cited By

Majumdar RSathiyanarayana V(2025)Sound and Complete Proof Rules for Probabilistic TerminationProceedings of the ACM on Programming Languages10.1145/37048999:POPL(1871-1902)Online publication date: 9-Jan-2025
https://dl.acm.org/doi/10.1145/3704899
Chatterjee KGoharshady ENovotný PŽikelić Đ(2024)Equivalence and Similarity Refutation for Probabilistic ProgramsProceedings of the ACM on Programming Languages10.1145/36564628:PLDI(2098-2122)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656462
Klinkenberg LBlumenthal CChen MHaase DKatoen J(2024)Exact Bayesian Inference for Loopy Probabilistic Programs using Generating FunctionsProceedings of the ACM on Programming Languages10.1145/36498448:OOPSLA1(923-953)Online publication date: 29-Apr-2024
https://dl.acm.org/doi/10.1145/3649844
Show More Cited By

Index Terms

Ranking and Repulsing Supermartingales for Reachability in Randomized Programs
1. Software and its engineering
  1. Software creation and management
    1. Software verification and validation
      1. Formal software verification
2. Theory of computation
  1. Models of computation
    1. Probabilistic computation

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Published In

cover image ACM Transactions on Programming Languages and Systems

ACM Transactions on Programming Languages and Systems Volume 43, Issue 2

June 2021

197 pages

ISSN:0164-0925

EISSN:1558-4593

DOI:10.1145/3470134

Editor:
Andrew Myers
Cornell University, USA

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Copyright © 2021 Owner/Author.

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

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 08 June 2021

Accepted: 01 February 2021

Revised: 01 January 2021

Received: 01 May 2019

Published in TOPLAS Volume 43, Issue 2

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Japan Science and Technology Agency
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Cited By

Majumdar RSathiyanarayana V(2025)Sound and Complete Proof Rules for Probabilistic TerminationProceedings of the ACM on Programming Languages10.1145/37048999:POPL(1871-1902)Online publication date: 9-Jan-2025
https://dl.acm.org/doi/10.1145/3704899
Chatterjee KGoharshady ENovotný PŽikelić Đ(2024)Equivalence and Similarity Refutation for Probabilistic ProgramsProceedings of the ACM on Programming Languages10.1145/36564628:PLDI(2098-2122)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656462
Klinkenberg LBlumenthal CChen MHaase DKatoen J(2024)Exact Bayesian Inference for Loopy Probabilistic Programs using Generating FunctionsProceedings of the ACM on Programming Languages10.1145/36498448:OOPSLA1(923-953)Online publication date: 29-Apr-2024
https://dl.acm.org/doi/10.1145/3649844
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
Majumdar RSathiyanarayana V(2024)Positive Almost-Sure Termination: Complexity and Proof RulesProceedings of the ACM on Programming Languages10.1145/36328798:POPL(1089-1117)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632879
Feng SYang TChen MZhan N(2024)A Unified Framework for Quantitative Analysis of Probabilistic ProgramsPrinciples of Verification: Cycling the Probabilistic Landscape10.1007/978-3-031-75783-9_10(230-254)Online publication date: 13-Nov-2024
https://doi.org/10.1007/978-3-031-75783-9_10
Abate AGiacobbe MRoy DSchnitzer Y(2024)Model Checking and Strategy Synthesis with Abstractions and CertificatesPrinciples of Verification: Cycling the Probabilistic Landscape10.1007/978-3-031-75775-4_16(360-391)Online publication date: 13-Nov-2024
https://doi.org/10.1007/978-3-031-75775-4_16
Matheja C(2024)A Game-Based Semantics for the Probabilistic Intermediate Verification Language HeyVLBridging the Gap Between AI and Reality10.1007/978-3-031-75434-0_17(242-258)Online publication date: 30-Dec-2024
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Chatterjee KGoharshady AGoharshady EKarrabi MŽikelić Đ(2024)Sound and Complete Witnesses for Template-Based Verification of LTL Properties on Polynomial ProgramsFormal Methods10.1007/978-3-031-71162-6_31(600-619)Online publication date: 11-Sep-2024
https://doi.org/10.1007/978-3-031-71162-6_31
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: 24-Jul-2024
https://dl.acm.org/doi/10.1007/978-3-031-65633-0_19
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