research-article

Polynomial invariant generation for non-deterministic recursive programs

Authors:

Krishnendu Chatterjee,

Amir Kafshdar Goharshady,

Ehsan Kafshdar GoharshadyAuthors Info & Claims

PLDI 2020: Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation

Pages 672 - 687

https://doi.org/10.1145/3385412.3385969

Published: 11 June 2020 Publication History

Abstract

We consider the classical problem of invariant generation for programs with polynomial assignments and focus on synthesizing invariants that are a conjunction of strict polynomial inequalities. We present a sound and semi-complete method based on positivstellensaetze, i.e. theorems in semi-algebraic geometry that characterize positive polynomials over a semi-algebraic set.

On the theoretical side, the worst-case complexity of our approach is subexponential, whereas the worst-case complexity of the previous complete method (Kapur, ACA 2004) is doubly-exponential. Even when restricted to linear invariants, the best previous complexity for complete invariant generation is exponential (Colon et al, CAV 2003). On the practical side, we reduce the invariant generation problem to quadratic programming (QCLP), which is a classical optimization problem with many industrial solvers. We demonstrate the applicability of our approach by providing experimental results on several academic benchmarks. To the best of our knowledge, the only previous invariant generation method that provides completeness guarantees for invariants consisting of polynomial inequalities is (Kapur, ACA 2004), which relies on quantifier elimination and cannot even handle toy programs such as our running example.

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Pirzada MReger GBhayat ACordeiro LFilkov VRay BZhou M(2024)LLM-Generated Invariants for Bounded Model Checking Without Loop UnrollingProceedings of the 39th IEEE/ACM International Conference on Automated Software Engineering10.1145/3691620.3695512(1395-1407)Online publication date: 27-Oct-2024
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Kura SUnno H(2024)Automated Verification of Higher-Order Probabilistic Programs via a Dependent Refinement Type SystemProceedings of the ACM on Programming Languages10.1145/36746628:ICFP(973-1002)Online publication date: 15-Aug-2024
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Bayarmagnai EMohammadi FPrébet R(2024)Algebraic Tools for Computing Polynomial Loop InvariantsProceedings of the 2024 International Symposium on Symbolic and Algebraic Computation10.1145/3666000.3669710(371-381)Online publication date: 16-Jul-2024
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Index Terms

Polynomial invariant generation for non-deterministic recursive programs
1. Theory of computation
  1. Logic
    1. Logic and verification
  2. Semantics and reasoning
    1. Program reasoning
      1. Invariants

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cover image ACM Conferences

PLDI 2020: Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation

June 2020

1174 pages

ISBN:9781450376136

DOI:10.1145/3385412

General Chair:
Alastair F. Donaldson
Imperial College London, UK
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Emina Torlak
University of Washington, USA

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Published: 11 June 2020

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National Natural Science Foundation of China
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PLDI '20: 41st ACM SIGPLAN International Conference on Programming Language Design and Implementation

June 15 - 20, 2020

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Overall Acceptance Rate 406 of 2,067 submissions, 20%

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Cited By

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https://dl.acm.org/doi/10.1145/3691620.3695512
Kura SUnno H(2024)Automated Verification of Higher-Order Probabilistic Programs via a Dependent Refinement Type SystemProceedings of the ACM on Programming Languages10.1145/36746628:ICFP(973-1002)Online publication date: 15-Aug-2024
https://dl.acm.org/doi/10.1145/3674662
Bayarmagnai EMohammadi FPrébet R(2024)Algebraic Tools for Computing Polynomial Loop InvariantsProceedings of the 2024 International Symposium on Symbolic and Algebraic Computation10.1145/3666000.3669710(371-381)Online publication date: 16-Jul-2024
https://dl.acm.org/doi/10.1145/3666000.3669710
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