Remarks on the Structural Grammatical Inference Problem for Context-Free Grammars

In the structural grammatical inference problem we try to infer a context-free grammar from its structural descriptions. This problem has recently been studied by Sakakibara [4,5]. As structural descriptions he uses derivation trees whose internal nodes are unlabelled. Given a sample, i.e. a set of words augmented by their unlabelled derivation trees, an algorithm solving the structural grammatical inference problem finds out a context-free grammar consistent with the sample. Sakakibara [51 has shown that for reversible context-free grammars there exists an algorithm which uses positive structural data only. A context-free grammar G = (V, _Z, P, S) is said to be rellersible if (1) A + (Y and B + CY in P implies A=B and (2) A-+aB/3 and A+dP in P implies B = C. The time complexity of Sakakibara’s algorithm and the structural grammatical inference problem for a subclass of reversible grammars are discussed in 131. Moreover, Sakakibara [4] has shown that if we allow structural membership queries and structural equivalence queries, then the whole class of context-free grammars can be inferred.