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
PublisherSpringer Verlag
Pages251-264
Number of pages14
Volume744 LNAI
ISBN (Print)9783540573708
Publication statusPublished - 1993
Externally publishedYes
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

Fingerprint

Threshold Circuits
VC Dimension
Threshold elements
Networks (circuits)
Point Sets
Upper and Lower Bounds
Lower bound
Upper bound
Output

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Sakurai, A. (1993). On the VC-dimension of depth four threshold circuits and the complexity of boolean-valued functions. In Algorithmic Learning Theory - 4th International Workshop, ALT 1993, Proceedings (Vol. 744 LNAI, 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.

On the VC-dimension of depth four threshold circuits and the complexity of boolean-valued functions. / Sakurai, Akito.

Algorithmic Learning Theory - 4th International Workshop, ALT 1993, Proceedings. Vol. 744 LNAI Springer Verlag, 1993. p. 251-264 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 744 LNAI).

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

Sakurai, A 1993, On the VC-dimension of depth four threshold circuits and the complexity of boolean-valued functions. in Algorithmic Learning Theory - 4th International Workshop, ALT 1993, Proceedings. vol. 744 LNAI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 744 LNAI, Springer Verlag, pp. 251-264, 4th Workshop on Algorithmic Learning Theory, ALT 1993, Tokyo, Japan, 93/11/8.
Sakurai A. On the VC-dimension of depth four threshold circuits and the complexity of boolean-valued functions. In Algorithmic Learning Theory - 4th International Workshop, ALT 1993, Proceedings. Vol. 744 LNAI. Springer Verlag. 1993. p. 251-264. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Sakurai, Akito. / On the VC-dimension of depth four threshold circuits and the complexity of boolean-valued functions. Algorithmic Learning Theory - 4th International Workshop, ALT 1993, Proceedings. Vol. 744 LNAI Springer Verlag, 1993. pp. 251-264 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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