Computational Complexity of Natural Languages: A Reasoned Overview

There has been an upsurge of research interest in natural language complexity. As this interest will benefit from being informed by established contributions in this area, this paper presents a reasoned overview of central results concerning the computational complexity of natural language parsing. This overview also seeks to help to understand why, contrary to recent and widespread assumptions, it is by no means sufficient that an agent handles sequences of items under a pattern $a^n b^n$ or under a pattern $a^n b^m c^n d^m$ to ascertain ipso facto that this is the result of at least an underlying context-free grammar or an underlying context-sensitive grammar, respectively. In addition, it seeks to help to understand why it is also not sufficient that an agent handles sequences of items under a pattern $a^n b^n$ for it to be deemed as having a cognitive capacity of higher computational complexity.