Horn upper bounds and renaming

Authors:
Marina Langlois;Robert H. Sloan;György Turán
Affiliations:
University of Illinois at Chicago, Chicago, IL;University of Illinois at Chicago, Chicago, IL;University of Illinois at Chicago, Chicago, IL
Venue:
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Year:
2007

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Abstract

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.