Annals of Mathematics and Artificial Intelligence

, Volume 1, Issue 1, pp 33–47

On renamable Horn and generalized Horn functions

  • Vijaya Chandru
  • Collette R. Coullard
  • Peter L. Hammer
  • Miguel Montañez
  • Xiaorong Sun
Article

DOI: 10.1007/BF01531069

Cite this article as:
Chandru, V., Coullard, C.R., Hammer, P.L. et al. Ann Math Artif Intell (1990) 1: 33. doi:10.1007/BF01531069

Abstract

A Boolean function in disjunctive normal form (DNF) is aHorn function if each of its elementary conjunctions involves at most one complemented variable. Ageneralized Horn function is constructed from a Horn function by disjuncting a nested set of complemented variables to it. The satisfiability problem is solvable in polynomial time for both Horn and generalized Horn functions. A Boolean function in DNF is said to berenamable Horn if it is Horn after complementation of some variables. Succinct mathematical characterizations and linear-time algorithms for recognizing renamable Horn and generalized Horn functions are given in this paper. The algorithm for recognizing renamable Horn functions gives a new method to test 2-SAT. Some computational results are also given.

Keywords

Computational logicHorn formulaegeneralized Horn formulae

Copyright information

© J.C. Baltzer A.G. Scientific Publishing Company 1990

Authors and Affiliations

  • Vijaya Chandru
    • 1
  • Collette R. Coullard
    • 1
  • Peter L. Hammer
    • 2
  • Miguel Montañez
    • 1
  • Xiaorong Sun
    • 2
  1. 1.School of Industrial EngineeringPurdue UniversityWest LafayetteUSA
  2. 2.RUTCOR-Rutgers Center for Operations ResearchRutgers UniversityNew BrunswickUSA