Combinatorial Problems for Horn Clauses

  • Authors:
  • Marina Langlois;Dhruv Mubayi;Robert H. Sloan;György Turán

  • Affiliations:
  • University of Illinois at Chicago, Chicago, USA;University of Illinois at Chicago, Chicago, USA;University of Illinois at Chicago, Chicago, USA;University of Illinois at Chicago, Chicago, USA and Hungarian Academy of Sciences & University of Szeged, Hungary

  • Venue:
  • Graph Theory, Computational Intelligence and Thought
  • Year:
  • 2009

Quantified Score

Hi-index 0.03

Visualization

Abstract

Given a family of Horn clauses, what is the minimal number of Horn clauses implying all other clauses in the family? What is the maximal number of Horn clauses from the family without having resolvents of a certain kind? We consider various problems of this type, and give some sharp bounds. We also consider the probability that a random family of a given size implies all other clauses in the family, and we prove the existence of a sharp threshold.