On the intrinsic complexity of language identification

  • Authors:
  • Sanjay Jain;Arun Sharma

  • Affiliations:
  • Department of Information Systems and Computer Science, National University of Singapore, Singapore 0511, Republic of Singapore;School of Computer Science and Engineering, The University of New South Wales, Sydney, NSW 2052, Australia

  • Venue:
  • COLT '94 Proceedings of the seventh annual conference on Computational learning theory
  • Year:
  • 1994

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Abstract

A new investigation of the complexity of language identification is undertaken using the notion of reduction from recursion theory and complexity theory. The approach, referred to as the intrinsic complexity of language identification, employs notions of “weak” and “strong” reduction between learnable classes of languages. The intrinsic complexity of several classes are considered and the results agree with the intuitive difficulty of learning these classes. Several complete classes are shown for both the reductions and it is also established that the weak and strong reductions are distinct.An interesting result is that the self referential class of Wiehagen in which the minimal element of every language is a grammar for the language and the class of pattern languages introduced by Angluin are equivalent in the strong sense.This study has been influenced by a similar treatment of function identification by Freivalds, Kinber, and Smith.