Horn Upper Bounds and Renaming

  • Marina Langlois
  • Robert H. Sloan
  • György Turán
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4501)


We consider the problem of computing tractable approximations to CNF formulas, extending the approach of Selman and Kautz to compute the Horn-LUB to involve renaming of variables. Negative results are given for the quality of approximation in this extended version. On the other hand, experiments for random 3-CNF show that the new algorithms improve both running time and approximation quality. The output sizes and approximation errors exhibit a ‘Horn bump’ phenomenon: unimodal patterns are observed with maxima in some intermediate range of densities. We also present the results of experiments generating pseudo-random satisfying assignments for Horn formulas.


Approximation Quality Truth Assignment Horn Clause Output Size Prime Implicants 
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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Marina Langlois
    • 1
  • Robert H. Sloan
    • 1
  • György Turán
    • 1
  1. 1.University of Illinois at Chicago, Chicago, IL 60607USA

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