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Decidable verification of uninterpreted programs

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Mahesh ViswanathanAuthors Info & Claims

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

Article No.: 46, Pages 1 - 29

https://doi.org/10.1145/3290359

Published: 02 January 2019 Publication History

Abstract

We study the problem of completely automatically verifying uninterpreted programs—programs that work over arbitrary data models that provide an interpretation for the constants, functions and relations the program uses. The verification problem asks whether a given program satisfies a postcondition written using quantifier-free formulas with equality on the final state, with no loop invariants, contracts, etc. being provided. We show that this problem is undecidable in general. The main contribution of this paper is a subclass of programs, called coherent programs that admits decidable verification, and can be decided in Pspace. We then extend this class of programs to classes of programs that are k-coherent, where k ∈ ℕ, obtained by (automatically) adding k ghost variables and assignments that make them coherent. We also extend the decidability result to programs with recursive function calls and prove several undecidability results that show why our restrictions to obtain decidability seem necessary.

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Elad NPadon OShoham S(2024)An Infinite Needle in a Finite Haystack: Finding Infinite Counter-Models in Deductive VerificationProceedings of the ACM on Programming Languages10.1145/36328758:POPL(970-1000)Online publication date: 5-Jan-2024
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Hong WChen ZZhang YYu HDu YWang J(2024)Verification of message-passing uninterpreted programsScience of Computer Programming10.1016/j.scico.2023.103075234:COnline publication date: 1-May-2024
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Nilizadeh ALeavens GKechagia MTan SMechtaev STan L(2022)Be realisticProceedings of the Third International Workshop on Automated Program Repair10.1145/3524459.3527346(31-32)Online publication date: 19-May-2022
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Index Terms

Decidable verification of uninterpreted programs
1. Theory of computation
  1. Logic
    1. Automated reasoning
    2. Logic and verification

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cover image Proceedings of the ACM on Programming Languages

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

January 2019

2275 pages

EISSN:2475-1421

DOI:10.1145/3302515

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Copyright © 2019 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: 02 January 2019

Published in PACMPL Volume 3, Issue POPL

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Cited By

Elad NPadon OShoham S(2024)An Infinite Needle in a Finite Haystack: Finding Infinite Counter-Models in Deductive VerificationProceedings of the ACM on Programming Languages10.1145/36328758:POPL(970-1000)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632875
Hong WChen ZZhang YYu HDu YWang J(2024)Verification of message-passing uninterpreted programsScience of Computer Programming10.1016/j.scico.2023.103075234:COnline publication date: 1-May-2024
https://dl.acm.org/doi/10.1016/j.scico.2023.103075
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https://dl.acm.org/doi/10.1145/3524459.3527346
Krogmeier PMadhusudan P(2022)Learning formulas in finite variable logicsProceedings of the ACM on Programming Languages10.1145/34986716:POPL(1-28)Online publication date: 12-Jan-2022
https://dl.acm.org/doi/10.1145/3498671
Du YHong WChen ZWang J(2022)Collaborative Verification of Uninterpreted ProgramsTheoretical Aspects of Software Engineering10.1007/978-3-031-10363-6_10(148-154)Online publication date: 8-Jul-2022
https://dl.acm.org/doi/10.1007/978-3-031-10363-6_10
Finkbeiner BHeim PPassing N(2022)Temporal Stream Logic modulo TheoriesFoundations of Software Science and Computation Structures10.1007/978-3-030-99253-8_17(325-346)Online publication date: 29-Mar-2022
https://doi.org/10.1007/978-3-030-99253-8_17
Hong WChen ZDu YWang J(2021)Trace Abstraction-Based Verification for Uninterpreted ProgramsFormal Methods10.1007/978-3-030-90870-6_29(545-562)Online publication date: 10-Nov-2021
https://doi.org/10.1007/978-3-030-90870-6_29
Narayanan AMathur AChetty MKshirsagar M(2020)Dark patternsCommunications of the ACM10.1145/339788463:9(42-47)Online publication date: 21-Aug-2020
https://dl.acm.org/doi/10.1145/3397884
Krogmeier PMathur UMurali AMadhusudan PViswanathan M(2020)Decidable Synthesis of Programs with Uninterpreted FunctionsComputer Aided Verification10.1007/978-3-030-53291-8_32(634-657)Online publication date: 21-Jul-2020
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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: 17-Apr-2020
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