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Matematicheskie Zametki, 2010, Volume 87, Issue 5, Pages 721–733
DOI: https://doi.org/10.4213/mzm8720 (Mi mzm8720) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Refined Estimates of the Number of Repetition-Free Boolean Functions in the Full Binary Basis {&,∨,⊕,−}

O. V. Zubkov

Irkutsk State Pedagogical University
Full-text PDF (507 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm8720
Abstract: We consider repetition-free Boolean functions in the basis {&,∨,⊕,−}, and prove a formula expressing the number of such functions of n variables as a product of Fibonacci numbers. These products are estimated; as a result, we obtain asymptotic estimates for the number of repetition-free Boolean functions. These estimates involve Euler numbers of second order and can be reduced by well-known methods to the form of an exponential-power series. These estimates can be used to construct the final asymptotics of the number of repetition-free Boolean functions in the full binary basis.
Keywords: repetition-free Boolean function, full binary basis, binary function, Fibonacci numbers, Euler numbers, index preserving structure.
Received: 26.09.2008
Revised: 22.10.2009
English version:
Mathematical Notes, 2010, Volume 87, Issue 5, Pages 687–699
DOI: https://doi.org/10.1134/S0001434610050081
Bibliographic databases:
Document Type: Article
UDC: 519.11+519.71
Language: Russian
Citation: O. V. Zubkov, “Refined Estimates of the Number of Repetition-Free Boolean Functions in the Full Binary Basis {&,∨,⊕,−}”, Mat. Zametki, 87:5 (2010), 721–733; Math. Notes, 87:5 (2010), 687–699
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm/v87/i5/p721
    • This publication is cited in the following 1 articles:
    1. V. A. Voblyi, “On the asymptotics of the number of repetition-free Boolean functions in the basis $\{\&,\lor,\oplus,\lnot\}$”, Discrete Math. Appl., 27:1 (2017), 55–56  mathnet  crossref  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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