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Diskr. Mat., 2008, Volume 20, Issue 3, Pages 51–72 (Mi dm1013)  

This article is cited in 1 scientific paper (total in 1 paper)

The fundamental difference between depth and delay

V. M. Khrapchenko


Abstract: Earlier, it was proved that even for a minimal circuit the delay $T$ could be much less than the depth $D$. Namely, an infinite sequence of minimal circuits was constructed such that $T<\log_2D+6$ and $D\to\infty$. This result would be more interesting if the inequality were true for all equivalent minimal circuits. In this paper, we present an infinite sequence of Boolean functions $F_k$, $k=1,2,…$, such that any minimal circuit for an arbitrary function $F_k$ has the depth and the delay obeying the inequality $T<\log_2D+14$.
This research was supported by the Program of Basic Research of Department of Applied Mathematics of Russian Academy of Sciences “Algebraic and Combinatorial Methods of Mathematical Cybernetics”, project “Design and Complexity of Control Systems”.

DOI: https://doi.org/10.4213/dm1013

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English version:
Discrete Mathematics and Applications, 2008, 18:4, 391–412

Bibliographic databases:

UDC: 519.95
Received: 02.07.2006

Citation: V. M. Khrapchenko, “The fundamental difference between depth and delay”, Diskr. Mat., 20:3 (2008), 51–72; Discrete Math. Appl., 18:4 (2008), 391–412

Citation in format AMSBIB
\Bibitem{Khr08}
\by V.~M.~Khrapchenko
\paper The fundamental difference between depth and delay
\jour Diskr. Mat.
\yr 2008
\vol 20
\issue 3
\pages 51--72
\mathnet{http://mi.mathnet.ru/dm1013}
\crossref{https://doi.org/10.4213/dm1013}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2467454}
\zmath{https://zbmath.org/?q=an:1174.94035}
\elib{http://elibrary.ru/item.asp?id=20730253}
\transl
\jour Discrete Math. Appl.
\yr 2008
\vol 18
\issue 4
\pages 391--412
\crossref{https://doi.org/10.1515/DMA.2008.029}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-53349172329}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. D. Korshunov, “Computational complexity of Boolean functions”, Russian Math. Surveys, 67:1 (2012), 93–165  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Дискретная математика
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