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Correlations between Horn fractions, satisfiability and solver performance for fixed density random 3-CNF instances

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Abstract

An enhanced concept of sub-optimal reverse Horn fraction of a CNF-formula was introduced in [18]. It was shown that this fraction is very useful in effectively (almost) separating 3-colorable random graphs with fixed node-edge density from the non-3-colorable ones. A correlation between this enhanced sub-optimal reverse Horn fraction and satisfiability of random 3-SAT instances with a fixed density was observed. In this paper, we present experimental evidence that this correlation scales to larger-sized instances and that it extends to solver performances as well, both of complete and incomplete solvers. Furthermore, we give a motivation for various phases in the algorithm aHS, establishing the enhanced sub-optimal reverse Horn fraction, and we present clear evidence for the fact that the observed correlations are stronger than correlations between satisfiability and sub-optimal MAXSAT-fractions established similarly to the enhanced sub-optimal reverse Horn fraction. The latter observation is noteworthy because the correlation between satisfiability and the optimal MAXSAT-fraction is obviously 100%.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Software Technology, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands

    Hans van Maaren & Linda van Norden

Authors
  1. Hans van Maaren
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  2. Linda van Norden
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Correspondence to Hans van Maaren.

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AMS subject classification

90C05, 03B99, 68Q01, 68W01

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van Maaren, H., van Norden, L. Correlations between Horn fractions, satisfiability and solver performance for fixed density random 3-CNF instances. Ann Math Artif Intell 44, 157–177 (2005). https://doi.org/10.1007/s10472-005-2369-1

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  • DOI: https://doi.org/10.1007/s10472-005-2369-1

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