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 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.
Keywordsautomata theory and formal languages structural descriptions grammatical inference
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- 5.De la Higuera, C.: Grammatical inference: learning automata and grammars. Cambridge University Press (2010)Google Scholar
- 7.Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation, 2nd edn. Pearson Addison Wesley (2003)Google Scholar
- 13.Sipser, M.: Introduction to the Theory of Computation, 2nd edn. Thomson (2006)Google Scholar