Complexity of computing Vapnik-Chervonenkis dimension

研究成果: Conference contribution

3 被引用数 (Scopus)

抄録

The Vapnik-Chervonenkis (VC) dimension is known to be the crucial measure of the polynomial-sample learnability in the PAC-learning model. This paper investigates the complexity of computing VC-dimension of a concept class over a finite learning domain. We consider a decision problem called the discrete VC-dimension problem which is, for a given matrix representing a concept class F and an integer K, to determine whether the VC-dimension of F is greater than K or not. We prove that (1) the discrete VC-dimension problem is polynomial-time reducible to the satisfiability problem of length J with O(log2J) variables, and (2) for every constant C, the satisfiability problem in conjunctive normal form with m clauses and Clog2m variables is polynomial-time reducible to the discrete VC-dimension problem. These results can be interpreted, in some sense, that the problem is “complete” for the class of nO(log n time computable sets.

本文言語English
ホスト出版物のタイトルAlgorithmic Learning Theory - 4th International Workshop, ALT 1993, Proceedings
編集者Klaus P. Jantke, Shigenobu Kobayashi, Etsuji Tomita, Takashi Yokomori
出版社Springer Verlag
ページ279-287
ページ数9
ISBN(印刷版)9783540573708
DOI
出版ステータスPublished - 1993
外部発表はい
イベント4th Workshop on Algorithmic Learning Theory, ALT 1993 - Tokyo, Japan
継続期間: 1993 11 81993 11 10

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
744 LNAI
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Other

Other4th Workshop on Algorithmic Learning Theory, ALT 1993
国/地域Japan
CityTokyo
Period93/11/893/11/10

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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