On the Structural Grammatical Inference Problem for Some Classes of Context-Free Grammars

Inference from positive data is strictly less powerful than inference from positive and negative data [l]. As a method for compensating for the lack of negative data, Sakakibara [7,8] has considered the problem of inferring context-free grammars from structural information. Given a finite positive sample, i.e. a set of words belonging to the language generated by the grammar in question, and the derivation trees of the words with unlabelled internal nodes, Sakakibara’s algorithm [7] finds out the reversible context-free grammar consistent with the sample. In other words, Sakakibara’s algorithm solves the structural grammatical inference problem for reversible grammars. A context-free grammar G = (V, Z, P, S> is said to be reversible if (1) A + (Y and B + a in P implies A = B and (2) A + (YB~ and A * aCp in P implies B = C. Hence, a context-free grammar is reversible if and only if it is (1) invertible and (2) reset-free. All context-free languages can be generated by reversible context-free grammars [7].