---
title: "Efficient Symmetry Breaking for Boolean Satisfiability"
authors:
  - "Fadi A. Aloul"
  - "Karem A. Sakallah"
  - "Igor L. Markov"
doi: ""
url: "https://ijcai.org/proceedings/2003/40"
pdf: "https://ijcai.org/proceedings/2003/0040.pdf"
venue: "Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence"
year: 2003
pages: "271-275"
track: ""
keywords:
---

# Efficient Symmetry Breaking for Boolean Satisfiability

Fadi A. Aloul, Karem A. Sakallah, Igor L. Markov

*Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence*, pages 271-275.

## Abstract

Identifying and breaking the symmetries of CNF formulae has been shown to lead to significant reductions in search times. In this paper we describe a more systematic and efficient construction of symmetry-breaking predicates (SBPs ). In particular, we use the cycle structure of symmetry generators, which typically involve very few variables, to drastically reduce the size of SBPs. Furthermore, our new SBP construction grows linearly with the number of relevant variables as opposed to the previous quadratic constructions. Our empirical data suggest that these improvements reduce search run times by one to two orders of magnitude on a wide variety of benchmarks with symmetries.