Scientific Annals of Computer Science

"Alexandru Ioan Cuza" University of Iaşi

Learning Cover Context-Free Grammars from Structural Data

Published in Volume XXIV, Issue 2, 2014, p. 253-286, doi: 10.7561/SACS.2014.2.253

Authors: M. Marin, G. Istrate


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 LA, 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 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.

Keywords: automata theory and formal languages, grammatical inference, structural descriptions

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