# On renamable Horn and generalized Horn functions

- First Online:

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 a*Horn function* if each of its elementary conjunctions involves at most one complemented variable. A*generalized 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 be*renamable 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.