We consider the problem of learning deterministic even linear language
s from positive examples, We show that, for any nonnegative integer k,
the class of LR(k) even linear languages is not learnable from positi
ve examples while there is a subclass called LRS(k), which is a natura
l subclass of LR(k) in the strong sense, learnable from positive examp
les. Our learning algorithm 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.