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Boolean Rings for Intersection-Based Satisfiability

  • Nachum Dershowitz
  • Jieh Hsiang
  • Guan-Shieng Huang
  • Daher Kaiss
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4246)

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.

Keywords

Gaussian Elimination Propositional Variable Boolean Formula Boolean Equation Boolean Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Nachum Dershowitz
    • 1
  • Jieh Hsiang
    • 2
  • Guan-Shieng Huang
    • 3
  • Daher Kaiss
    • 4
  1. 1.School of Computer ScienceTel Aviv UniversityRamat AvivIsrael
  2. 2.Department of Computer Science and Information EngineeringNational Taiwan UniversityTaipeiTaiwan
  3. 3.Department of Computer Science and Information EngineeringNational Chi Nan UniversityNantouTaiwan
  4. 4.Design Technology Solutions GroupIntel CorporationHaifaIsrael

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