Minimal Comparison of Octagonal Abstract Domains

2026-06-13

AI Summary

This work addresses the inconsistency in invariant precision caused by varying expressiveness among numerical abstract domains in static program analysis, where accurate minimal comparison requires eliminating spurious constraints from abstract states. The paper presents the first efficient algorithm for removing such spurious constraints specifically tailored to the Octagon abstract domain. Grounded in abstract interpretation theory, the approach integrates constraint graph analysis with redundancy detection techniques to effectively identify and eliminate redundant constraints. Experimental evaluation on 6,930 invariants demonstrates that the method substantially mitigates precision loss stemming from the inherent limitations of octagonal expressiveness, enabling a large number of previously misclassified invariants to be correctly recognized as equivalent. Consequently, this work successfully extends minimal comparison techniques to more expressive numerical abstract domains.

Abstract

Numerical abstract domains vary in their expressiveness; more expressive domains like Zones yield more precise invariants than Intervals. A comprehensive approach to selecting abstract domains is a minimal comparison of abstract states. However, to be effective, it requires abstract states to be free of spurious constraints. While previous work developed spurious constraint elimination for Zones, this work introduces a novel algorithm for eliminating such constraints for Octagons. We evaluate our approach by comparing the precision of 6,930 invariants from different abstract domains. Our results show that the minimal comparison reclassifies many invariants as equivalent, thus reducing the impact of Octagons' expressiveness on invariant precision.

Problem

• abstract domains
• spurious constraints
• Octagons
• minimal comparison
• invariant precision

Innovation

• Octagons
• spurious constraint elimination
• abstract domains
• minimal comparison
• numerical invariants