Complexity of computing Vapnik-Chervonenkis dimension

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

3 Citations (Scopus)


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.

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
Number of pages9
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


Other4th Workshop on Algorithmic Learning Theory, ALT 1993

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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