On renamable Horn and generalized Horn functions
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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.
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Annals of Mathematics and Artificial Intelligence
Volume 1, Issue 1-4 , pp 33-47
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- Springer Netherlands
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- Computational logic
- Horn formulae
- generalized Horn formulae
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- Author Affiliations
- 1. School of Industrial Engineering, Purdue University, 47907, West Lafayette, IN, USA
- 2. RUTCOR-Rutgers Center for Operations Research, Rutgers University, 08903, New Brunswick, NJ, USA