Combinatorial OptimizationView this Special Issue
Renato Bruni, "On the orthogonalization of arbitrary Boolean formulae", Advances in Decision Sciences, vol. 2005, Article ID 247409, 14 pages, 2005. https://doi.org/10.1155/JAMDS.2005.61
On the orthogonalization of arbitrary Boolean formulae
The orthogonal conjunctive normal form of a Boolean function is a conjunctive normal form in which any two clauses contain at least a pair of complementary literals. Orthogonal disjunctive normal form is defined similarly. Orthogonalization is the process of transforming the normal form of a Boolean function to orthogonal normal form. The problem is of great relevance in several applications, for example, in the reliability theory. Moreover, such problem is strongly connected with the well-known propositional satisfiability problem. Therefore, important complexity issues are involved. A general procedure for transforming an arbitrary CNF or DNF to an orthogonal one is proposed. Such procedure is tested on randomly generated Boolean formulae.
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