The Complexity of Learning Principles and Parameters Grammars

TL;DR

This paper explores the computational complexity of learning context-free and context-sensitive grammars, introducing a new subclass inspired by psycholinguistic theories and proving their inherent learning difficulties.

Contribution

It introduces principled parametric grammars modeling psycholinguistic principles and demonstrates their computational hardness in learning scenarios.

Findings

PPCFGs are not efficiently learnable with equivalence and membership oracles.

PPCFGs are not efficiently learnable from positive data unless P=NP.

PPCSGs are not efficiently learnable unless integer factorization is in P.

Abstract

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.