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Minimally Comparing Relational Abstract Domains

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Automated Technology for Verification and Analysis (ATVA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14216))

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Abstract

Value-based static analysis techniques express computed program invariants as logical formula over program variables. Researchers and practitioners use these invariants to aid in software engineering and verification tasks. When selecting abstract domains, practitioners weigh the cost of a domain against its expressiveness. However, an abstract domain’s expressiveness tends to be stated in absolute terms; either mathematically via the sub-polyhedra the domain is capable of describing, empirically using a set of known properties to verify, or empirically via logical entailment using the entire invariant of the domain at each program point. Due to carry-over effects, however, the last technique can be problematic because it tends to provide simplistic and imprecise comparisons.

We address these limitations of comparing, in general, abstract domains via logical entailment in this work. We provide a fixed-point algorithm for including the minimally necessary variables from each domain into the compared formula. Furthermore, we empirically evaluate our algorithm, comparing different techniques of widening over the Zones domain and comparing Zones to an incomparable Relational Predicates domain. Our empirical evaluation of our technique shows an improved granularity of comparison. It lowered the number of more precise invariants when comparing analysis techniques, thus, limiting the prevalent carry-over effects. Moreover, it removed undecidable invariants and lowered the number of incomparable invariants when comparing two incomparable relational abstract domain.

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Notes

  1. 1.

    \(z \le x\) is included due to transitive effects through \(x\).

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Acknowledgments

The work reported here was supported by the U.S. National Science Foundation under award CCF-19-42044.

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Authors and Affiliations

  1. Boise State University, Boise, USA

    Kenny Ballou & Elena Sherman

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  1. Kenny Ballou
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  2. Elena Sherman
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Correspondence to Kenny Ballou .

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Editors and Affiliations

  1. Université Sorbonne Paris Nord, Villetaneuse, France

    Étienne André

  2. Singapore Management University, Singapore, Singapore

    Jun Sun

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Ballou, K., Sherman, E. (2023). Minimally Comparing Relational Abstract Domains. In: André, É., Sun, J. (eds) Automated Technology for Verification and Analysis. ATVA 2023. Lecture Notes in Computer Science, vol 14216. Springer, Cham. https://doi.org/10.1007/978-3-031-45332-8_8

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  • DOI: https://doi.org/10.1007/978-3-031-45332-8_8

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