On the VC-dimension of depth four threshold circuits and the complexity of boolean-valued functions

Akito Sakurai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

We consider the problem of determining VC-dimension (Formula Found) of depth four n-input 1-output threshold circuits with h elements. Best known asymptotic lower bounds and upper bounds are proved, that is, when (Formula Found) is upper bounded by ((h2/3)+nh(log h)(1+o(1)) and lower bounded by (1/2)((h2/4)+nh)(log h)(1 − o(1)). We also consider the problem of determining complexity c3(N) of Boolean-valued functions defined on N-pointsets in Rn, measured by the number of threshold elements, with which we can construct a depth four circuit to realize the functions. We also show the best known upper and lower bounds, that is, when N → ∞, the complexity is upper bounded by (Formula Found) and lower bounded by (Formula Found)

Original languageEnglish
Title of host publicationAlgorithmic Learning Theory - 4th International Workshop, ALT 1993, Proceedings
EditorsKlaus P. Jantke, Shigenobu Kobayashi, Etsuji Tomita, Takashi Yokomori
PublisherSpringer Verlag
Pages251-264
Number of pages14
ISBN (Print)9783540573708
DOIs
Publication statusPublished - 1993 Jan 1
Event4th Workshop on Algorithmic Learning Theory, ALT 1993 - Tokyo, Japan
Duration: 1993 Nov 81993 Nov 10

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume744 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other4th Workshop on Algorithmic Learning Theory, ALT 1993
CountryJapan
CityTokyo
Period93/11/893/11/10

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Sakurai, A. (1993). On the VC-dimension of depth four threshold circuits and the complexity of boolean-valued functions. In K. P. Jantke, S. Kobayashi, E. Tomita, & T. Yokomori (Eds.), Algorithmic Learning Theory - 4th International Workshop, ALT 1993, Proceedings (pp. 251-264). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 744 LNAI). Springer Verlag. https://doi.org/10.1007/3-540-57370-4_52