research-article

Proof Spaces for Unbounded Parallelism

Authors:

Zachary Kincaid,

Andreas PodelskiAuthors Info & Claims

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

Pages 407 - 420

https://doi.org/10.1145/2676726.2677012

Published: 14 January 2015 Publication History

Abstract

In this paper, we present a new approach to automatically verify multi-threaded programs which are executed by an unbounded number of threads running in parallel.

The starting point for our work is the problem of how we can leverage existing automated verification technology for sequential programs (abstract interpretation, Craig interpolation, constraint solving, etc.) for multi-threaded programs. Suppose that we are given a correctness proof for a trace of a program (or for some other program fragment). We observe that the proof can always be decomposed into a finite set of Hoare triples, and we ask what can be proved from the finite set of Hoare triples using only simple combinatorial inference rules (without access to a theorem prover and without the possibility to infer genuinely new Hoare triples)?

We introduce a proof system where one proves the correctness of a multi-threaded program by showing that for each trace of the program, there exists a correctness proof in the space of proofs that are derivable from a finite set of axioms using simple combinatorial inference rules. This proof system is complete with respect to the classical proof method of establishing an inductive invariant (which uses thread quantification and control predicates). Moreover, it is possible to algorithmically check whether a given set of axioms is sufficient to prove the correctness of a multi-threaded program, using ideas from well-structured transition systems.

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Cited By

Farzan AKlumpp DPodelski A(2024)Commutativity Simplifies Proofs of Parameterized ProgramsProceedings of the ACM on Programming Languages10.1145/36329258:POPL(2485-2513)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632925
Farzan A(2023)Commutativity in Automated Verification2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS56636.2023.10175734(1-7)Online publication date: 26-Jun-2023
https://doi.org/10.1109/LICS56636.2023.10175734
Pani TWeissenbacher GZuleger F(2023)Thread-modular counter abstraction: automated safety and termination proofs of parameterized software by reduction to sequential program verificationFormal Methods in System Design10.1007/s10703-023-00439-664:1-3(108-145)Online publication date: 6-Oct-2023
https://doi.org/10.1007/s10703-023-00439-6
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Index Terms

Proof Spaces for Unbounded Parallelism
1. Software and its engineering
  1. Software creation and management
    1. Software verification and validation
      1. Formal software verification
  2. Software organization and properties
    1. Software functional properties
      1. Correctness
      2. Formal methods
2. Theory of computation
  1. Logic
    1. Proof theory

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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
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Copyright © 2015 ACM.

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Published: 14 January 2015

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Ontario Ministry of Research
Natural Sciences and Engineering Research Council of Canada
Deutsche Forschungsgemeinschaft

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SIGPLAN

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

January 15 - 17, 2015

Mumbai, India

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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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POPL '25

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The 52nd Annual ACM SIGPLAN Symposium on Principles of Programming Languages

January 19 - 25, 2025

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Cited By

Farzan AKlumpp DPodelski A(2024)Commutativity Simplifies Proofs of Parameterized ProgramsProceedings of the ACM on Programming Languages10.1145/36329258:POPL(2485-2513)Online publication date: 5-Jan-2024
Farzan A(2023)Commutativity in Automated Verification2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS56636.2023.10175734(1-7)Online publication date: 26-Jun-2023
Pani TWeissenbacher GZuleger F(2023)Thread-modular counter abstraction: automated safety and termination proofs of parameterized software by reduction to sequential program verificationFormal Methods in System Design10.1007/s10703-023-00439-664:1-3(108-145)Online publication date: 6-Oct-2023
Long TRen XWang QWang C(2022)Verifying the safety properties of distributed systems via mergeable parallelismJournal of Systems Architecture10.1016/j.sysarc.2022.102646130(102646)Online publication date: Sep-2022
Bloem RKhalimov AJacobs SKonnov IVeith HWidder JRubin S(2022)Decidability of Parameterized VerificationundefinedOnline publication date: 2-Apr-2022
Long TRen XWang QWang C(2021)Verifying the Correctness of Distributed Systems via Mergeable ParallelismDependable Software Engineering. Theories, Tools, and Applications10.1007/978-3-030-91265-9_7(122-140)Online publication date: 25-Nov-2021
Mathur UMadhusudan PViswanathan M(2020)What’s Decidable About Program Verification Modulo Axioms?Tools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-030-45237-7_10(158-177)Online publication date: 25-Apr-2020
Farzan AVandikas A(2019)Reductions for safety proofsProceedings of the ACM on Programming Languages10.1145/33710814:POPL(1-28)Online publication date: 20-Dec-2019
Mathur UMadhusudan PViswanathan M(2019)Decidable verification of uninterpreted programsProceedings of the ACM on Programming Languages10.1145/32903593:POPL(1-29)Online publication date: 2-Jan-2019
Feldman YWilcox JShoham SSagiv M(2019)Inferring Inductive Invariants from Phase StructuresComputer Aided Verification10.1007/978-3-030-25543-5_23(405-425)Online publication date: 12-Jul-2019
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