# On renamable Horn and generalized Horn functions

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## 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.

### Keywords

Computational logic Horn formulae generalized Horn formulae## Preview

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