Thue's 1914 paper: a translation

TL;DR

This paper provides a translation and analysis of Thue's 1914 work, emphasizing its historical significance in formal language theory, undecidability, and early computational concepts, with notes on its influence on the development of algorithms and formal systems.

Contribution

It offers the first comprehensive translation and contextual analysis of Thue's 1914 paper, highlighting its foundational role in formal language theory and computational logic.

Findings

Thue's paper contains early examples of undecidable problems.

It illustrates the transition from algebra to formal language theory.

The paper discusses the development of algorithms for rule generation.

Abstract

This paper includes notes to accompany a reading of Thue's 1914 paper "Probleme uber Veranderungen von Zeichenreihen nach gegebenen Reglen", along with a translation of that paper. Thue's 1914 paper is mainly famous for proving an early example of an undecidable problem, cited prominently by Post. However, Post's paper principally makes use of the definition of Thue systems, described on the first two pages of Thue's paper, and does not depend on the more specific results in the remainder of Thue's paper. A closer study of the remaining parts of that paper highlight a number of important themes in the history of computing: the transition from algebra to formal language theory, the analysis of the "computational power" (in a pre-1936 sense) of rules, and the development of algorithms to generate rule-sets.