Advances in Decision Sciences

Advances in Decision Sciences / 2005 / Article
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Combinatorial Optimization

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Volume 2005 |Article ID 247409 | https://doi.org/10.1155/JAMDS.2005.61

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

Received15 Oct 2002
Revised19 Mar 2004

Abstract

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.

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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