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Uspekhi Mat. Nauk, 2012, Volume 67, Issue 1(403), Pages 97–168 (Mi umn9459)  

This article is cited in 3 scientific papers (total in 3 papers)

Computational complexity of Boolean functions

A. D. Korshunov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: Boolean functions are among the fundamental objects of discrete mathematics, especially in those of its subdisciplines which fall under mathematical logic and mathematical cybernetics. The language of Boolean functions is convenient for describing the operation of many discrete systems such as contact networks, Boolean circuits, branching programs, and some others. An important parameter of discrete systems of this kind is their complexity. This characteristic has been actively investigated starting from Shannon's works. There is a large body of scientific literature presenting many fundamental results. The purpose of this survey is to give an account of the main results over the last sixty years related to the complexity of computation (realization) of Boolean functions by contact networks, Boolean circuits, and Boolean circuits without branching.
Bibliography: 165 titles.

Keywords: basis, Boolean circuits, Boolean function, depth and delay of a Boolean circuit, disjunctive normal form, invariant classes of Boolean functions, cellular circuits, contact network without zero chains, logical formulae, lower bounds for the complexity of circuits, series-parallel contact network, symmetric Boolean function, complexity of a circuit, partial Boolean function.

DOI: https://doi.org/10.4213/rm9459

Full text: PDF file (1086 kB)
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English version:
Russian Mathematical Surveys, 2012, 67:1, 93–165

Bibliographic databases:

UDC: 519.95+519.7
MSC: Primary 06E30, 68Q30, 94C10; Secondary 06E99
Received: 04.10.2011

Citation: A. D. Korshunov, “Computational complexity of Boolean functions”, Uspekhi Mat. Nauk, 67:1(403) (2012), 97–168; Russian Math. Surveys, 67:1 (2012), 93–165

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Yu. V. Maximov, “Implementation of Boolean functions with a bounded number of zeros by disjunctive normal forms”, Comput. Math. Math. Phys., 53:9 (2013), 1391–1409  mathnet  crossref  crossref  isi  elib  elib
    2. Chikalov I., Hussain Sh., Moshkov M., “Totally optimal decision trees for Boolean functions”, Discrete Appl. Math., 215 (2016), 1–13  crossref  mathscinet  zmath  isi  elib  scopus
    3. AbouEisha H., Amin T., Chikalov I., Hussain Sh., Moshkov M., “Multi-Stage Optimization of Decision Trees With Some Applications”: AbouEisha, H Amin, T Chikalov, I Hussain, S Moshkov, M, Extensions of Dynamic Programming For Combinatorial Optimization and Data Mining, Intelligent Systems Reference Library, 146, Springer-Verlag Berlin, 2019, 49–71  crossref  mathscinet  isi  scopus
  • Успехи математических наук Russian Mathematical Surveys
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