The Complexity of Learning Principles and Parameters Grammars

We investigate models for learning the class of context-free and context-sensitive languages (CFLs and CSLs). We begin with a brief discussion of some early hardness results which show that unrestricted language learning is impossible, and unrestricted CFL learning is computationally infeasible; we then briefly survey the literature on algorithms for learning restricted subclasses of the CFLs. Finally, we introduce a new family of subclasses, the principled parametric context-free grammars (and a corresponding family of principled parametric context-sensitive grammars), which roughly model the "Principles and Parameters" framework in psycholinguistics. We present three hardness results: first, that the PPCFGs are not efficiently learnable given equivalence and membership oracles, second, that the PPCFGs are not efficiently learnable from positive presentations unless P = NP, and third, that the PPCSGs are not efficiently learnable from positive presentations unless integer factorization is in P.