A Fresh Look at Zones and Octagons

Author:

Gange Graeme1ORCID,Ma Zequn2,Navas Jorge A.3ORCID,Schachte Peter2ORCID,Søndergaard Harald2ORCID,Stuckey Peter J.1ORCID

Affiliation:

1. Monash University, Clayton, Australia

2. The University of Melbourne, Parkville, Australia

3. SRI International, CA, USA

Abstract

Zones and Octagons are popular abstract domains for static program analysis. They enable the automated discovery of simple numerical relations that hold between pairs of program variables. Both domains are well understood mathematically but the detailed implementation of static analyses based on these domains poses many interesting algorithmic challenges. In this article, we study the two abstract domains, their implementation and use. Utilizing improved data structures and algorithms for the manipulation of graphs that represent difference-bound constraints, we present fast implementations of both abstract domains, built around a common infrastructure. We compare the performance of these implementations against alternative approaches offering the same precision. We quantify the differences in performance by measuring their speed and precision on standard benchmarks. We also assess, in the context of software verification, the extent to which the improved precision translates to better verification outcomes. Experiments demonstrate that our new implementations improve the state of the art for both Zones and Octagons significantly.

Funder

Australian Research Council under Discovery Early Career Researcher Award

U.S. National Science Foundation

Publisher

Association for Computing Machinery (ACM)

Subject

Software

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Strided Difference Bound Matrices;Lecture Notes in Computer Science;2024

2. Minimally Comparing Relational Abstract Domains;Automated Technology for Verification and Analysis;2023

3. Octagons Revisited;Static Analysis;2023

4. Identifying Minimal Changes in the Zone Abstract Domain;Theoretical Aspects of Software Engineering;2023

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