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Partial (In)Completeness in abstract interpretation: limiting the imprecision in program analysis

Authors:

Mila Dalla Preda,

Roberto GiacobazziAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 6, Issue POPL

Article No.: 59, Pages 1 - 31

https://doi.org/10.1145/3498721

Published: 12 January 2022 Publication History

Abstract

Imprecision is inherent in any decidable (sound) approximation of undecidable program properties. In abstract interpretation this corresponds to the release of false alarms, e.g., when it is used for program analysis and program verification. As all alarming systems, a program analysis tool is credible when few false alarms are reported. As a consequence, we have to live together with false alarms, but also we need methods to control them. As for all approximation methods, also for abstract interpretation we need to estimate the accumulated imprecision during program analysis. In this paper we introduce a theory for estimating the error propagation in abstract interpretation, and hence in program analysis. We enrich abstract domains with a weakening of a metric distance. This enriched structure keeps coherence between the standard partial order relating approximated objects by their relative precision and the effective error made in this approximation. An abstract interpretation is precise when it is complete. We introduce the notion of partial completeness as a weakening of precision. In partial completeness the abstract interpreter may produce a bounded number of false alarms. We prove the key recursive properties of the class of programs for which an abstract interpreter is partially complete with a given bound of imprecision. Then, we introduce a proof system for estimating an upper bound of the error accumulated by the abstract interpreter during program analysis. Our framework is general enough to be instantiated to most known metrics for abstract domains.

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Cited By

Liew DCogumbreiro TLange J(2024)Sound and Partially-Complete Static Analysis of Data-Races in GPU ProgramsProceedings of the ACM on Programming Languages10.1145/36897978:OOPSLA2(2434-2461)Online publication date: 8-Oct-2024
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Giacobazzi RMastroeni IPerantoni E(2024)Adversities in Abstract Interpretation - Accommodating Robustness by Abstract InterpretationACM Transactions on Programming Languages and Systems10.1145/364930946:2(1-31)Online publication date: 24-Feb-2024
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Index Terms

Partial (In)Completeness in abstract interpretation: limiting the imprecision in program analysis
1. Theory of computation

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 6, Issue POPL

January 2022

1886 pages

EISSN:2475-1421

DOI:10.1145/3511309

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Copyright © 2022 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: 12 January 2022

Published in PACMPL Volume 6, Issue POPL

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Cited By

Liew DCogumbreiro TLange J(2024)Sound and Partially-Complete Static Analysis of Data-Races in GPU ProgramsProceedings of the ACM on Programming Languages10.1145/36897978:OOPSLA2(2434-2461)Online publication date: 8-Oct-2024
https://dl.acm.org/doi/10.1145/3689797
Holter KHennoste JLam PSaan SVojdani VEdwards JTaeumel M(2024)Abstract Debuggers: Exploring Program Behaviors using Static Analysis ResultsProceedings of the 2024 ACM SIGPLAN International Symposium on New Ideas, New Paradigms, and Reflections on Programming and Software10.1145/3689492.3690053(130-146)Online publication date: 17-Oct-2024
https://dl.acm.org/doi/10.1145/3689492.3690053
Giacobazzi RMastroeni IPerantoni E(2024)Adversities in Abstract Interpretation - Accommodating Robustness by Abstract InterpretationACM Transactions on Programming Languages and Systems10.1145/364930946:2(1-31)Online publication date: 24-Feb-2024
https://dl.acm.org/doi/10.1145/3649309
Campion MDalla Preda MGiacobazzi RUrban C(2024)Monotonicity and the Precision of Program AnalysisProceedings of the ACM on Programming Languages10.1145/36328978:POPL(1629-1662)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632897
Bruni RGiacobazzi RGori RRanzato F(2023)Local Completeness in Abstract InterpretationChallenges of Software Verification10.1007/978-981-19-9601-6_8(145-156)Online publication date: 22-Jul-2023
https://doi.org/10.1007/978-981-19-9601-6_8
Jurjo DMorales JLopez-Garcia PHermenegildo M(2023)A Rule-Based Approach for Designing and Composing Abstract DomainsLogic-Based Program Synthesis and Transformation10.1007/978-3-031-45784-5_6(80-98)Online publication date: 23-Oct-2023
https://dl.acm.org/doi/10.1007/978-3-031-45784-5_6

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