Syntactic Structures and Code Parameters

TL;DR

This paper explores the application of error-correcting codes to syntactic structures of languages, revealing their distribution in code parameter space and how language change models can influence code properties.

Contribution

It introduces a novel approach of assigning error-correcting codes to syntactic data and analyzes their distribution, including codes surpassing classical bounds, and studies language change dynamics through spin glass models.

Findings

Many codes lie above classical bounds like Gilbert-Varshamov and Plotkin.

Language change dynamics can improve code parameters under certain entailment relations.

Analysis of large language sets reveals insights into spin glass dynamics.

Abstract

We assign binary and ternary error-correcting codes to the data of syntactic structures of world languages and we study the distribution of code points in the space of code parameters. We show that, while most codes populate the lower region approximating a superposition of Thomae functions, there is a substantial presence of codes above the Gilbert-Varshamov bound and even above the asymptotic bound and the Plotkin bound. We investigate the dynamics induced on the space of code parameters by spin glass models of language change, and show that, in the presence of entailment relations between syntactic parameters the dynamics can sometimes improve the code. For large sets of languages and syntactic data, one can gain information on the spin glass dynamics from the induced dynamics in the space of code parameters.