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Cybernetics and Systems Analysis

, Volume 55, Issue 1, pp 30–33 | Cite as

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

  • A. I. TimoshkinEmail author
Article
  • 2 Downloads

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.

Keywords

implicant lattice order-convex subset ideal coideal 

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References

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    M. M. Kovalev, Matroids in Discrete Optimization [in Russian], Universitetskoe, Minsk (1987).Google Scholar
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    G. Birkhoff, Lattice Theory [Russian translation], Nauka, Moscow (1984).Google Scholar
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    S. V. Yablonskii, Introduction to Discrete Mathematics [in Russian], Nauka, Moscow (1986).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.National Metallurgical Academy of UkraineDniproUkraine

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