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Clausal Congruence Closure

Authors Armin Biere , Katalin Fazekas , Mathias Fleury , Nils Froleyks

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Author Details

Armin Biere
  • University Freiburg, Germany
Katalin Fazekas
  • TU Wien, Austria
Mathias Fleury
  • University Freiburg, Germany
Nils Froleyks
  • Johannes Kepler University, Linz, Austria

Funding

This work was supported by the state of Baden-Württemberg through bwHPC, the German Research Foundation (DFG) through grant INST 35/1597-1 FUGG, the Austrian Science Fund (FWF) under project No. T-1306, and by a gift from Intel Corporation.

Acknowledgements

Finally, we want to thank the anonymous reviewers for valuable comments and useful suggestions, which definitely helped us to improve the paper considerably, particularly in the exposition of the experimental part.

Cite AsGet BibTex

Armin Biere, Katalin Fazekas, Mathias Fleury, and Nils Froleyks. Clausal Congruence Closure. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 6:1-6:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.SAT.2024.6

Abstract

Many practical applications of satisfiability solving employ multiple steps to encode an original problem formulation into conjunctive normal form. Often circuits are used as intermediate representation before encoding those circuits into clausal form. These circuits however might contain redundant isomorphic sub-circuits. If blindly translated into clausal form, this redundancy is retained and increases solving time unless specific preprocessing algorithms are used. Furthermore, such redundant sub-formula structure might only emerge during solving and needs to be addressed by inprocessing. This paper presents a new approach which extracts gate information from the formula and applies congruence closure to match and eliminate redundant gates. Besides new algorithms for gate extraction, we also describe previous unpublished attempts to tackle this problem. Experiments focus on the important problem of combinational equivalence checking for hardware designs and show that our new approach yields a substantial gain in CNF solver performance.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automated reasoning
Keywords
  • Satisfiability Solving
  • Congruence Closure
  • Structural Hashing
  • SAT Sweeping
  • Conjunctive Normal Form
  • Combinational Equivalence Checking
  • Hardware Equivalence Checking

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Supplementary Materials

References

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