Minimal Comparison of Octagonal Abstract Domains

2026-06-16 · Source: cs.SE updates on arXiv.org · Field: Science & Research — Mathematics & Computational Sciences, Engineering & Applied Sciences · Depth: Expert, extended

Summary

This work introduces a novel algorithm for eliminating spurious constraints for Octagons, a numerical abstract domain. The approach evaluates its effectiveness by comparing the precision of 6,930 invariants from different abstract domains. Results demonstrate that a minimal comparison technique, when combined with the new spurious constraint reduction algorithm (MN+Reduction), significantly reclassifies many invariants as equivalent. For Octagons versus Intervals, the proportion of Octagon invariants deemed more precise dropped from 86% (full comparison) to 36%. Similarly, for Octagons versus Zones, this proportion decreased from 26% to 6%. When comparing Octagons with the incomparable Symbolic Predicates domain, equivalent invariants increased from 17% to 54%, and all 11 previously UNKNOWN queries were resolved due to reduced query size. These findings suggest that Octagons often compute predominantly interval invariants.

Key takeaway

For research scientists evaluating abstract domain precision in static analysis, you should integrate spurious constraint reduction into your comparison methodology. Traditional full comparisons overestimate Octagon precision, as shown by reclassifying many invariants as equivalent. Applying the novel Algorithm 2 for Octagons, combined with minimal comparison, provides a more accurate view of precision benefits, especially for incomparable domains, and can resolve previously "UNKNOWN" SMT solver queries.

Key insights

A novel algorithm for spurious constraint reduction in Octagon abstract domains improves minimal comparison of invariant precision.

Principles

• Spurious constraints decrease the precision of finding minimal state changes.
• Fully closed abstract states can contain spurious dependencies between variables.
• Octagon abstract domains often compute predominantly interval-valued invariants.

Method

The paper presents Algorithm 2, an $O(N^2)$ constraint reduction algorithm for Octagons, which removes redundant couplings by setting spurious constraint values to +∞ before applying Algorithm 1 for minimal variable identification.

In practice

• Apply Algorithm 2 to Octagon DBMs before performing minimal invariant comparisons.
• Use minimal comparison with reduction to resolve "UNKNOWN" queries in SMT solvers.
• Re-evaluate abstract domain precision claims by incorporating spurious constraint reduction.

Topics

• Octagon Abstract Domain
• Spurious Constraint Elimination
• Static Program Analysis
• Data-Flow Analysis
• Invariant Precision
• Abstract Interpretation

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.SE updates on arXiv.org.