We consider the problem of learning an unknown context-free grammar when the
only knowledge available and of interest to the learner is about its structural
descriptions with depth at most ℓ. The goal is to learn a cover
context-free grammar (CCFG) with respect to ℓ, that is, a CFG whose
structural descriptions with depth at most ℓ agree with those of the
unknown CFG. We propose an algorithm, called LAℓ, that efficiently learns
a CCFG using two types of queries: structural equivalence and structural
membership. We show that LAℓ runs in time polynomial in the number of
states of a minimal deterministic finite cover tree automaton (DCTA) with
respect to ℓ. This number is often much smaller than the number of states
of a minimum deterministic finite tree automaton for the structural
descriptions of the unknown grammar