An Algorithm for Constructing Reduced DNFs of Order-Convex Boolean Functions

This paper considers the problem of constructing reduced disjunctive normal forms of order-convex Boolean functions. An original algorithm is proposed for finding these forms. The algorithm uses concepts of the theory of ordered sets such as an ideal and a coideal and has a substantially lower time...

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Vydáno v:	Cybernetics and systems analysis Ročník 55; číslo 1; s. 30 - 33
Hlavní autor:	Timoshkin, A. I.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.01.2019 Springer Springer Nature B.V
Témata:	Algorithms Artificial Intelligence Boolean Boolean algebra Boolean functions Control Mathematics Mathematics and Statistics Processor Architectures Software Engineering/Programming and Operating Systems Systems Theory implicant coideal ideal order-convex subset lattice
ISSN:	1060-0396, 1573-8337
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Abstract	This paper considers the problem of constructing reduced disjunctive normal forms of order-convex Boolean functions. An original algorithm is proposed for finding these forms. The algorithm uses concepts of the theory of ordered sets such as an ideal and a coideal and has a substantially lower time complexity than the classical Quine–McCluskey algorithm.
AbstractList	This paper considers the problem of constructing reduced disjunctive normal forms of order-convex Boolean functions. An original algorithm is proposed for finding these forms. The algorithm uses concepts of the theory of ordered sets such as an ideal and a coideal and has a substantially lower time complexity than the classical Quine-McCluskey algorithm. This paper considers the problem of constructing reduced disjunctive normal forms of order-convex Boolean functions. An original algorithm is proposed for finding these forms. The algorithm uses concepts of the theory of ordered sets such as an ideal and a coideal and has a substantially lower time complexity than the classical Quine-McCluskey algorithm. Keywords: implicant, lattice, order-convex subset, ideal, coideal.
Audience	Academic
Author	Timoshkin, A. I.
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Copyright	Springer Science+Business Media, LLC, part of Springer Nature 2019 COPYRIGHT 2019 Springer Cybernetics and Systems Analysis is a copyright of Springer, (2019). All Rights Reserved.
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DOI	10.1007/s10559-019-00109-8
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References	BirkhoffGLattice Theory [Russian translation]1984MoscowNauka KovalevMMMatroids in Discrete Optimization [in Russian]1987MinskUniversitetskoe AignerMCombinatorial Theory [Russian translation]1982MoscowMir YablonskiiSVIntroduction to Discrete Mathematics [in Russian]1986MoscowNauka M Aigner (109_CR1) 1982 SV Yablonskii (109_CR4) 1986 MM Kovalev (109_CR2) 1987 G Birkhoff (109_CR3) 1984
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SubjectTerms	Algorithms Artificial Intelligence Boolean Boolean algebra Boolean functions Control Mathematics Mathematics and Statistics Processor Architectures Software Engineering/Programming and Operating Systems Systems Theory
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Title	An Algorithm for Constructing Reduced DNFs of Order-Convex Boolean Functions
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