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Matematicheskie Zametki, 1971, Volume 10, Issue 1, Pages 83–92 (Mi mzm7071)  

This article is cited in 50 scientific papers (total in 51 papers)

Method of determining lower bounds for the complexity of P-schemes

V. M. Khrapchenko

Institute for Applied Mathematics, USSR Academy of Sciences
Abstract: A method of calculating lower bounds, quadratic in the arguments of the function, for the complexity of P-schemes.
Received: 27.07.1970
English version:
Mathematical Notes, 1971, Volume 10, Issue 1, Pages 474–479
DOI: https://doi.org/10.1007/BF01747074
Bibliographic databases:
UDC: 51.0116
Language: Russian
Citation: V. M. Khrapchenko, “Method of determining lower bounds for the complexity of P-schemes”, Mat. Zametki, 10:1 (1971), 83–92; Math. Notes, 10:1 (1971), 474–479
Citation in format AMSBIB
\Bibitem{Khr71}
\by V.~M.~Khrapchenko
\paper Method of determining lower bounds for the complexity of $P$-schemes
\jour Mat. Zametki
\yr 1971
\vol 10
\issue 1
\pages 83--92
\mathnet{http://mi.mathnet.ru/mzm7071}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=287982}
\zmath{https://zbmath.org/?q=an:0223.68009}
\transl
\jour Math. Notes
\yr 1971
\vol 10
\issue 1
\pages 474--479
\crossref{https://doi.org/10.1007/BF01747074}
Linking options:
  • https://www.mathnet.ru/eng/mzm7071
  • https://www.mathnet.ru/eng/mzm/v10/i1/p83
  • This publication is cited in the following 51 articles:
    1. K. L. Rychkov, “O stroenii odnogo klassa sovershennykh Π-razbienii”, Sib. elektron. matem. izv., 20:2 (2023), 1499–1518  mathnet  crossref
    2. Or Meir, 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS), 2023, 1056  crossref
    3. Magnus Gausdal Find, Alexander Golovnev, Edward A. Hirsch, Alexander S. Kulikov, “Improving 3N Circuit Complexity Lower Bounds”, comput. complex., 32:2 (2023)  crossref
    4. K. L. Rychkov, “Predstavleniya normalizovannykh formul”, Diskretn. analiz i issled. oper., 29:4 (2022), 77–103  mathnet  crossref  mathscinet
    5. Jiatu Li, Tianqi Yang, Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing, 2022, 1180  crossref
    6. I. S. Sergeev, “Formula Complexity of a Linear Function in a k-ary Basis”, Math. Notes, 109:3 (2021), 445–458  mathnet  crossref  crossref  isi  elib
    7. Valentine Kabanets, Sajin Koroth, Zhenjian Lu, Dimitrios Myrisiotis, Igor C. Oliveira, “Algorithms and Lower Bounds for De Morgan Formulas of Low-Communication Leaf Gates”, ACM Trans. Comput. Theory, 13:4 (2021), 1  crossref
    8. S. B. Gashkov, I. S. Sergeev, “O znachenii rabot V. M. Khrapchenko”, PDM, 2020, no. 48, 109–124  mathnet  crossref
    9. Susanna F. de Rezende, Or Meir, Jakob Nordstrom, Toniann Pitassi, Robert Robere, 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS), 2020, 43  crossref
    10. K. L. Rychkov, “O sovershennosti minimalnykh pravilnykh razbienii mnozhestva reber n-mernogo kuba”, Diskretn. analiz i issled. oper., 26:4 (2019), 74–107  mathnet  crossref
    11. K. L. Rychkov, “Complexity of the realization of a linear Boolean function in the class of π-schemes”, J. Appl. Industr. Math., 12:3 (2018), 540–576  mathnet  crossref  crossref  elib
    12. Alexander Golovnev, Edward A. Hirsch, Alexander Knop, Alexander S. Kulikov, “On the limits of gate elimination”, Journal of Computer and System Sciences, 96 (2018), 107  crossref
    13. I. S. Sergeev, “Upper bounds for the size and the depth of formulae for MOD-functions”, Discrete Math. Appl., 27:1 (2017), 15–22  mathnet  crossref  crossref  mathscinet  isi  elib
    14. Magnus Gausdal Find, Alexander Golovnev, Edward A. Hirsch, Alexander S. Kulikov, 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS), 2016, 89  crossref
    15. K. L. Rychkov, “Sufficient conditions for the minimal π-schemes for linear Boolean functions to be locally non-repeating”, J. Appl. Industr. Math., 9:4 (2015), 580–587  mathnet  crossref  crossref  mathscinet  elib
    16. I. S. Sergeev, “Upper bounds on the formula size of symmetric Boolean functions”, Russian Math. (Iz. VUZ), 58:5 (2014), 30–42  mathnet  crossref
    17. S. B. Gashkov, E. T. Shavgulidze, “Representation of monomials as a sum of powers of linear forms”, Moscow University Mathematics Bulletin, 69:2 (2014), 51–55  mathnet  crossref  mathscinet
    18. Yu. L. Vasil'ev, K. L. Rychkov, “A lower bound on formula size of a ternary linear function”, J. Appl. Industr. Math., 7:4 (2013), 588–596  mathnet  crossref  mathscinet
    19. V. M. Khrapchenko, “A simplified proof of a lower complexity estimate”, Discrete Math. Appl., 23:2 (2013), 171–174  mathnet  crossref  crossref  mathscinet  elib
    20. Ilan Komargodski, Ran Raz, Proceedings of the forty-fifth annual ACM symposium on Theory of Computing, 2013, 171  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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