Learning cover context-free grammars from structural data

Abstract

We consider the problem of learning an unknown contextfree grammar when the only knowledge available and of interest to the learner is about its structural descriptions with depth at most 2113ℓ. 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.