Exploiting structure in symmetry detection for CNF

• Published in: 2004 41st Conference Design Automation pp. 530 - 534
• Main Authors: Darga, Paul T., Liffiton, Mark H., Sakallah, Karem A., Markov, Igor L.
• Format: Conference Proceeding
• Language: English
• Published: New York, NY, USA ACM 07.06.2004; IEEE; Association for Computing Machinery
• Series: ACM Conferences
• Subjects: Abstract algebra; Applied sciences; Boolean functions; Circuit synthesis; Computer architecture; Design. Technologies. Operation analysis. Testing; Electronic design automation and methodology; Electronics; Exact sciences and technology; Integrated circuits; Laboratories; Mathematics of computing > Discrete mathematics > Graph theory > Graph algorithms; Packaging; Partitioning algorithms; Permission; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Space exploration; partition refinement; graph automorphism; abstract algebra; boolean satisfiability (SAT); symmetry; backtrack search; Performance evaluation; Circuit design; Electronic packaging; Algorithm; Computer aided design; Satisfiability; Execution time
• ISBN: 1581138288; 9781581138283; 1511838288
• ISSN: 0738-100X
• DOI: 10.1145/996566.996712

Instances of the Boolean satisfiability problem (SAT) arise in many areas of circuit design and verification. These instances are typically constructed from some human-designed artifact, and thus are likely to possess much inherent symmetry and sparsity. Previous work[4] has shown that exploiting symmetries results in vastly reduced SAT solver run times, often with the search for the symmetries themselves dominating the total SAT solving time. Our contribution is twofold. First, we dissect the algorithms behind the venerable NAUTY[9] package, particularly the partition refinement procedure responsible for the majority of search space pruning as well as the majority of run time overhead. Second, we present a new symmetry-detection tool, SAUCY, which outperforms NAUTY by several orders of magnitude on the large, structured CNF formulas generated from typical EDA problems.