Learning Cover Context-Free Grammars from Structural Data

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 LA, that efficiently learns a CCFG using two types of queries: structural equivalence and structural membership. We show that LA 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.