Learning Cover Context-Free Grammars from Structural Data

Abstract

We consider the problem of learning an unknown context-free gram- mar from its structural descriptions with depth at most ℓ. The structural descriptions of the context-free grammar are its unlabelled derivation trees. 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. The learning proto- col is based on what is called in the literature a "minimally adequate teacher." 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.