Boolean rings for intersection-based satisfiability

  • Authors:

  • Nachum Dershowitz;Jieh Hsiang;Guan-Shieng Huang;Daher Kaiss

  • Affiliations:

  • School of Computer Science, Tel Aviv University, Ramat Aviv, Israel;Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan;Department of Computer Science and Information Engineering, National Chi Nan University, Nantou, Taiwan;Design Technology Solutions Group, Intel Corporation, Haifa, Israel

  • Venue:
  • LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
  • Year:
  • 2006

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Abstract

A potential advantage of using a Boolean-ring formalism for propositional formulæ is the large measure of simplification it facilitates. We propose a combined linear and binomial representation for Boolean-ring polynomials with which one can easily apply Gaussian elimination and Horn-clause methods to advantage. We demonstrate that this framework, with its enhanced simplification, is especially amenable to intersection-based learning, as in recursive learning and the method of Stålmarck. Experiments support the idea that problem variables can be eliminated and search trees can be shrunk by incorporating learning in the form of Boolean-ring saturation.