research-article

Proof Spaces for Unbounded Parallelism

Authors:

Zachary Kincaid,

Andreas PodelskiAuthors Info & Claims

ACM SIGPLAN Notices, Volume 50, Issue 1

Pages 407 - 420

https://doi.org/10.1145/2775051.2677012

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

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/s10703-023-00439-6Online publication date: 6-Oct-2023
https://doi.org/10.1007/s10703-023-00439-6
Iosif RXu X(2019)Alternating Automata Modulo First Order TheoriesComputer Aided Verification10.1007/978-3-030-25543-5_3(43-63)Online publication date: 12-Jul-2019
https://doi.org/10.1007/978-3-030-25543-5_3
Liu PWahl TLal A(2019)Verifying Asynchronous Event-Driven Programs Using Partial Abstract TransformersComputer Aided Verification10.1007/978-3-030-25543-5_22(386-404)Online publication date: 12-Jul-2019
https://doi.org/10.1007/978-3-030-25543-5_22
Show More Cited By

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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Published In

cover image ACM SIGPLAN Notices

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

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

Copyright © 2015 ACM.

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Association for Computing Machinery

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Publication History

Published: 14 January 2015

Published in SIGPLAN Volume 50, Issue 1

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Ontario Ministry of Research
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Cited By

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/s10703-023-00439-6Online publication date: 6-Oct-2023
https://doi.org/10.1007/s10703-023-00439-6
Iosif RXu X(2019)Alternating Automata Modulo First Order TheoriesComputer Aided Verification10.1007/978-3-030-25543-5_3(43-63)Online publication date: 12-Jul-2019
https://doi.org/10.1007/978-3-030-25543-5_3
Liu PWahl TLal A(2019)Verifying Asynchronous Event-Driven Programs Using Partial Abstract TransformersComputer Aided Verification10.1007/978-3-030-25543-5_22(386-404)Online publication date: 12-Jul-2019
https://doi.org/10.1007/978-3-030-25543-5_22
Farzan AVandikas A(2019)Automated Hypersafety VerificationComputer Aided Verification10.1007/978-3-030-25540-4_11(200-218)Online publication date: 12-Jul-2019
https://doi.org/10.1007/978-3-030-25540-4_11
Murphy CKincaid Z(2019)A Practical Algorithm for Structure EmbeddingVerification, Model Checking, and Abstract Interpretation10.1007/978-3-030-11245-5_16(342-362)Online publication date: 11-Jan-2019
https://doi.org/10.1007/978-3-030-11245-5_16
Iosif RXu X(2018)Abstraction Refinement for Emptiness Checking of Alternating Data AutomataTools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-319-89963-3_6(93-111)Online publication date: 14-Apr-2018
https://doi.org/10.1007/978-3-319-89963-3_6
Iosif RRogalewicz AVojnar T(2016)Abstraction Refinement and Antichains for Trace Inclusion of Infinite State SystemsProceedings of the 22nd International Conference on Tools and Algorithms for the Construction and Analysis of Systems - Volume 963610.1007/978-3-662-49674-9_5(71-89)Online publication date: 2-Apr-2016
https://dl.acm.org/doi/10.1007/978-3-662-49674-9_5
Holík LMeyer R(2016)Antichains for the Verification of Recursive ProgramsNetworked Systems10.1007/978-3-319-26850-7_22(322-336)Online publication date: 23-Mar-2016
https://doi.org/10.1007/978-3-319-26850-7_22
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
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