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Short XORs for Model Counting: From Theory to Practice

  • Carla P. Gomes
  • Joerg Hoffmann
  • Ashish Sabharwal
  • Bart Selman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4501)

Abstract

A promising approach for model counting was recently introduced, which in theory requires the use of large random xor or parity constraints to obtain near-exact counts of solutions to Boolean formulas. In practice, however, short xor constraints are preferred as they allow better constraint propagation in SAT solvers. We narrow this gap between theory and practice by presenting experimental evidence that for structured problem domains, very short xor constraints can lead to probabilistic variance as low as large xor constraints, and thus provide the same correctness guarantees. We initiate an understanding of this phenomenon by relating it to structural properties of synthetic instances.

Keywords

Conjunctive Normal Form Model Count Satisfying Assignment Solution Count Circuit Synthesis 
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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References

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    Gomes, C.P., Sabharwal, A., Selman, B.: Model counting: A new strategy for obtaining good bounds. In: 21th AAAI, Boston, MA, pp. 54–61 (2006)Google Scholar
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    Valiant, L.G., Vazirani, V.V.: NP is as easy as detecting unique solutions. Theoretical Comput. Sci. 47(3), 85–93 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
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    Bayardo Jr., R.J., Pehoushek, J.D.: Counting models using connected components. In: 17th AAAI, Austin, TX, pp. 157–162 (2000)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Carla P. Gomes
    • 1
  • Joerg Hoffmann
    • 2
  • Ashish Sabharwal
    • 1
  • Bart Selman
    • 1
  1. 1.Dept. of Computer Science, Cornell University, Ithaca NY 14853-7501U.S.A
  2. 2.University of Innsbruck, Technikerstraße 21a, 6020 InnsbruckAustria

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