Density condensation of boolean formulas

  • Authors:

  • Youichi Hanatani;Takashi Horiyama;Kazuo Iwama

  • Affiliations:

  • Graduate School of Informatics, Kyoto University, Kyoto, Japan;Graduate School of Informatics, Kyoto University, Kyoto, Japan;Graduate School of Informatics, Kyoto University, Kyoto, Japan

  • Venue:
  • Discrete Applied Mathematics - Special issue: Discrete algorithms and optimization, in honor of professor Toshihide Ibaraki at his retirement from Kyoto University
  • Year:
  • 2006

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Abstract

The following problem is considered: given a Boolean formula f, generate another formula g such that: (i) If f is unsatisfiable then g is also unsatisfiable. (ii) If f is satisfiable then g is also satisfiable and furthermore g is "easier" than f. For the measure of this easiness, we use the density, of a formula f which is defined as (the number of satisfying assignments)/2n, where n is the number of Boolean variables of f. In this paper, we mainly consider the case that the input formula f is given as a 3-CNF formula and the output formula g may be any formula using Boolean AND, OR and negation. Two different approaches to this problem are presented: one is to obtain g by reducing the number of variables and the other by increasing the number of variables, both of which are based on existing SAT algorithms. Our performance evaluation shows that, a little surprisingly, better SAT algorithms do not always give us better density-condensation algorithms.