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Russian Mathematical Surveys, 2012, Volume 67, Issue 1, Pages 93–165
DOI: https://doi.org/10.1070/RM2012v067n01ABEH004777 (Mi rm9459) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Computational complexity of Boolean functions

A. D. Korshunov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
English version PDF (978 kB) Citations (6)
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DOI: https://doi.org/10.1070/RM2012v067n01ABEH004777
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.
Received: 04.10.2011
Russian version:
Uspekhi Matematicheskikh Nauk, 2012, Volume 67, Issue 1(403), Pages 97–168
DOI: https://doi.org/10.4213/rm9459
Bibliographic databases:
Document Type: Article
UDC: 519.95+519.7
MSC: Primary 06E30, 68Q30, 94C10; Secondary 06E99
Language: English
Original paper language: Russian
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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    Remarks
    This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:137
    First page:76
     
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