Iterative learning of simple external contextual languages

  • Authors:
  • Leonor Becerra-Bonache;John Case;Sanjay Jain;Frank Stephan

  • Affiliations:
  • Department of Computer Science, Yale University, New Haven, CT 06520-8285, United States;Department of Computer and Information Sciences, University of Delaware, Newark, DE 19716-2586, United States;Department of Computer Science, National University of Singapore, Singapore 117417, Republic of Singapore;Department of Computer Science, National University of Singapore, Singapore 117417, Republic of Singapore and Department of Mathematics, National University of Singapore, Singapore 119076, Republi ...

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2010

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Abstract

It is investigated for which choice of a parameter q, denoting the number of contexts, the class of simple external contextual languages is iteratively learnable. On the one hand, the class admits, for all values of q, polynomial time learnability provided an adequate choice of the hypothesis space is given. On the other hand, additional constraints like consistency and conservativeness or the use of a one-one hypothesis space changes the picture - iterative learning limits the long term memory of the learner to the current hypothesis and these constraints further hinder storage of information via padding of this hypothesis. It is shown that if q3, then simple external contextual languages are not iteratively learnable using a class preserving one-one hypothesis space, while for q=1 it is iteratively learnable, even in polynomial time. It is also investigated for which choice of the parameters the simple external contextual languages can be learnt by a consistent and conservative iterative learner.