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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Bibliographic Details
Published in:Cybernetics and systems analysis Vol. 55; no. 1; pp. 30 - 33
Main Author: Timoshkin, A. I.
Format: Journal Article
Language:English
Published: New York Springer US 01.01.2019
Springer
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-019-00109-8