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Probabilistic Termination: Soundness, Completeness, and Compositionality

Authors:

Luis María Ferrer Fioriti,

Holger HermannsAuthors Info & Claims

POPL '15: Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

Pages 489 - 501

https://doi.org/10.1145/2676726.2677001

Published: 14 January 2015 Publication History

Abstract

We propose a framework to prove almost sure termination for probabilistic programs with real valued variables. It is based on ranking supermartingales, a notion analogous to ranking functions on non-probabilistic programs. The framework is proven sound and complete for a meaningful class of programs involving randomization and bounded nondeterminism. We complement this foundational insigh by a practical proof methodology, based on sound conditions that enable compositional reasoning and are amenable to a direct implementation using modern theorem provers. This is integrated in a small dependent type system, to overcome the problem that lexicographic ranking functions fail when combined with randomization. Among others, this compositional methodology enables the verification of probabilistic programs outside the complete class that admits ranking supermartingales.

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Cited By

Haselwarter PLi Kde Medeiros MGregersen SAguirre ATassarotti JBirkedal L(2024)Tachis: Higher-Order Separation Logic with Credits for Expected CostsProceedings of the ACM on Programming Languages10.1145/36897538:OOPSLA2(1189-1218)Online publication date: 8-Oct-2024
https://dl.acm.org/doi/10.1145/3689753
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
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
Show More Cited By

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Probabilistic Termination: Soundness, Completeness, and Compositionality

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cover image ACM Conferences

POPL '15: Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

January 2015

716 pages

ISBN:9781450333009

DOI:10.1145/2676726

General Chair:
Sriram Rajamani
Microsoft Research, India
,
Program Chair:
David Walker
Princeton University, USA

ACM SIGPLAN Notices Volume 50, Issue 1
POPL '15
January 2015
682 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/2775051
Editor:
Andy Gill
University of Kansas, Lawrence, KS
Issue’s Table of Contents

Copyright © 2015 Owner/Author.

Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Published: 14 January 2015

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January 15 - 17, 2015

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POPL '15 Paper Acceptance Rate 52 of 227 submissions, 23%;

Overall Acceptance Rate 824 of 4,130 submissions, 20%

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Cited By

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https://dl.acm.org/doi/10.1145/3689753
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
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
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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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Majumdar RSathiyanarayana V(2024)Sound and Complete Techniques for Reasoning About TerminationPrinciples of Verification: Cycling the Probabilistic Landscape10.1007/978-3-031-75783-9_2(41-72)Online publication date: 13-Nov-2024
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Kassing JGiesl J(2024)Annotated Dependency Pairs for Full Almost-Sure Termination of Probabilistic Term RewritingPrinciples of Verification: Cycling the Probabilistic Landscape10.1007/978-3-031-75783-9_14(339-366)Online publication date: 13-Nov-2024
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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
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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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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
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