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, USA CT 06520-8285;Department of Computer and Information Sciences, University of Delaware, Newark, USA DE 19716-2586;Department of Computer Science, National University of Singapore, Singapore, Republic of Singapore 117590;Department of Computer Science and Department of Mathematics, National University of Singapore, Singapore, Republic of Singapore 117543
Venue:
ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
Year:
2008

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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 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 q 3, 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. For the intermediate levels, there is some indication that iterative learnability using a class preserving one-one hypothesis space might depend on the size of the alphabet. 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.