Orthologic for SAT Solving

2026-05-14

AI Summary

This work addresses the problem of formula entailment in orthogonal logic and proposes a novel algorithm that avoids costly preprocessing while significantly improving practical efficiency without worsening worst-case time complexity. Leveraging this algorithm, the study presents the first reduction from orthogonal logic to generate hard SAT instances that admit short proofs yet remain highly challenging for modern SAT solvers. Experimental results demonstrate that the generated benchmarks substantially outperform state-of-the-art solvers such as Kissat on EPFL arithmetic circuits. Furthermore, the proposed method can serve as an effective preprocessing step to accelerate the solving of several difficult SAT instances.

Abstract

We present a new algorithm for deciding formula entailment in orthologic (a sound approximation of classical logic) that avoids the costly preprocessing phase of prior implementations while retaining the same $\mathcal{O}(n^2(1+|A|))$ worst-case complexity. We then introduce a family of synthetic SAT benchmarks based on the observation that, for any formula $φ$, the equivalence $φ\leftrightarrow \mathrm{NF}_{\mathrm{OL}}(φ)$ is a tautology whose Tseitin encoding yields unsatisfiable instances that are hard for state-of-the-art SAT solvers yet have short orthologic proofs. Applied to EPFL arithmetic circuits, our algorithm solves these instances efficiently while Kissat times out on a significant fraction. Finally, we show that using orthologic normalization as a preprocessing step can improve SAT solving time on some hard problems.

Problem

• orthologic
• SAT solving
• formula entailment
• benchmark generation
• normalization

Innovation

• orthologic
• SAT solving
• normalization
• synthetic benchmarks
• formula entailment