Polynomial Time Probabilistic Learning of a Subclass of Linear Languages with Queries

Authors:
Yasuhiro Tajima;Yoshiyuki Kotani
Affiliations:
Department of Computer and Information Sciences, Tokyo University of Agriculture and Technology, Tokyo, Japan 184-8588;Department of Computer and Information Sciences, Tokyo University of Agriculture and Technology, Tokyo, Japan 184-8588
Venue:
ICGI '08 Proceedings of the 9th international colloquium on Grammatical Inference: Algorithms and Applications
Year:
2008

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Abstract

We show a probabilistic learnability of a subclass of linear languages with queries. Learning via queries is an important problem in grammatical inference but the power of queries to probabilistic learnability is not clear yet. In probabilistic learning model, PAC (Probably Approximately Correct) criterion is an important one and many results have been shown in this model. Angluin has shown the ability of replacement from equivalence queries to random examples in PAC criterion but there are also many hardness results. We have shown that the class of simple deterministic languages is polynomial time learnable from membership queries and a representative sample. Also, we have shown that a representative sample can be constructed from polynomial number of random examples with the confidence probability. In this paper, we newly define a subclass of linear languages called strict deterministic linear languages and show the probabilistic learnability with membership queries in polynomial time. This learnability is derived from an exact learning algorithm for this subclass with membership queries, equivalence queries and a representative sample.