On the size of maximum renamable Horn sub-CNF

  • Authors:

  • Petr Kučera

  • Affiliations:

  • Department of Theoretical Computer Science and Mathematical Logic, Charles University, Malostranské Námstí 25, 118 00 Praha 1, Czech Republic

  • Venue:
  • Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
  • Year:
  • 2005

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Abstract

In [Boros, Discrete Appl. Math. 96/97 (1999) 29-40] a lower bound was shown for the size of a maximum renamable Horn sub-CNF of a given CNF. In this short note we show that this bound is tight for complete d-regular formulae on d variables. In fact, we show that this bound is tight even for the size of a maximum q-Horn subformula of a given complete d-regular formulae on d variables; the result for renamable Horn subformulae follows.