Abstract

We show that simple deterministic languages are polynomial time learnable via membership queries if the learner knows a special finite set of positive examples. This finite set is called a representative sample and has been introduced by Angluin Inform. Control 51 (1981) to show that regular languages are polynomial time learnable via membership queries. If simple deterministic languages are learnable in polynomial time via membership and equivalence queries, we can obtain a representative sample of a target language in polynomial time from a correct hypothesis. Thus, our result implies that the polynomial time learning problem of simple deterministic languages via membership and equivalence queries is solvable if and only if we can find a representative sample in polynomial time via these queries. We show the learnability of simple deterministic languages by giving a learning algorithm. The algorithm, at the first stage, makes all possible candidate rules to generate the target language and a set of simple deterministic grammars which are little different each other. Then, comparing them, the algorithm eliminates inappropriate rules.

Keywords: Grammatical inference; Learning via queries; Context-free language; Simple deterministic grammar; Representative sample