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XOR Local Search for Boolean Brent Equations

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Theory and Applications of Satisfiability Testing – SAT 2021 (SAT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12831))

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Abstract

Combining clausal and XOR reasoning has been studied for almost two decades, in particular in the context of CDCL and look-ahead, but not in classical local search. To stimulate research in this direction, we propose to standardize a hybrid format, called XNF, which allows both clauses and XORs. We implemented a tool to extract XOR constraints from a CNF, simplify them, and produce an XNF formula. The usefulness of XNF formulas is demonstrated by focusing on the impact of combined clausal and XOR reasoning on local search. Native support for XOR facilitates satisfying any falsified long XOR using a single flip, similarly to satisfying a falsified clause. When combined with XOR-based heuristics, local search performance is significantly improved on matrix multiplication challenges which are hard for CDCL.

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Notes

  1. 1.

    https://github.com/marijnheule/matrix-challenges.

  2. 2.

    https://www.msoos.org/xor-clauses/.

  3. 3.

    We are not aware of any formal publication about this format.

  4. 4.

    https://github.com/arminbiere/satch.

  5. 5.

    https://github.com/arminbiere/cnf2xnf.

  6. 6.

    also available at https://github.com/arminbiere/cnf2xnf.

  7. 7.

    https://github.com/Vtec234/xnfsat.

  8. 8.

    A detailed explanation of strategies in YalSAT is out of the scope of this paper.

  9. 9.

    The CNF encoding was generated by using XOR_p_4 on the handcrafted XNF.

  10. 10.

    In the final version, we will replace this note by a link to the full experimental data.

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Acknowledgements

The authors acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources that have contributed to the research results reported within this paper. The work is also supported by the National Science Foundation (NSF) under grant CCF-2010951, Austrian Science Fund (FWF), NFN S11408-N23 (RiSE), and the LIT AI Lab funded by the State of Upper Austria.

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Authors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, USA

    Wojciech Nawrocki, Zhenjun Liu & Marijn J. H. Heule

  2. Johannes Kepler University, Linz, Austria

    Andreas Fröhlich & Armin Biere

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  1. Wojciech Nawrocki
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  4. Marijn J. H. Heule
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Correspondence to Wojciech Nawrocki .

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  1. Laboratoire MIS, University of Picardie Jules Verne, Amiens, France

    Chu-Min Li

  2. IIIA-CSIC, Spanish National Research Council (CSIC), Bellaterra, Barcelona, Spain

    Felip Manyà

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Nawrocki, W., Liu, Z., Fröhlich, A., Heule, M.J.H., Biere, A. (2021). XOR Local Search for Boolean Brent Equations. In: Li, CM., Manyà, F. (eds) Theory and Applications of Satisfiability Testing – SAT 2021. SAT 2021. Lecture Notes in Computer Science(), vol 12831. Springer, Cham. https://doi.org/10.1007/978-3-030-80223-3_29

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