  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.
