Canonical Context-Free Grammars and Strong Learning: Two Approaches

Strong learning of context-free grammars is the problem of learning a grammar which is not just weakly equivalent to a target grammar but isomorphic or structurally equivalent to it. This is closely related to the problem of defining a canonical grammar for the language. The current proposal for strong learning of a small class of CFGs uses grammars whose nonterminals correspond to congruence classes of the language, in particular to a subset of those that satisfy a primality condition. Here we extend this approach to larger classes of CFGs where the nonterminals correspond instead to closed sets of strings; to elements of the syntactic concept lattice. We present two different classes of canonical context-free grammars. One is based on all of the primes in the lattice: the other, more suitable for strong learning algorithms is based on a subset of primes that are irreducible in a certain sense.