Learning Strongly Deterministic Even Linear Languages from Positive Examples

We consider the problem of learning deterministic even linear languages from positive examples. By a “deterministic” even linear language we mean a language generated by an LR(k) even linear grammar. We introduce a natural subclass of LR(k) even linear languages, called LR(k) in the strong sense, and show that this subclass is learnable in the limit from positive examples. Furthermore, we propose a learning algorithm that identifies this subclass in the limit with almost linear time in updating conjectures. As a corollary, in terms of even linear grammars, we have a learning algorithm for k-reversible languages that is more efficient than the one proposed by Angluin[Ang82].