Notes on Fragments of First-Order Concatenation Theory

TL;DR

This paper explores various decidable and undecidable segments of first-order concatenation theory, providing a universal axiomatization and normal-form results to better understand its logical structure.

Contribution

It introduces a complete universal axiomatization for certain fragments and establishes normal-form results, advancing the theoretical understanding of concatenation theory.

Findings

Identified decidable and undecidable fragments

Provided a universal axiomatization for these fragments

Proved normal-form results for the theory

Abstract

We identify a number of decidable and undecidable fragments of first-order concatenation theory. We also give a purely universal axiomatization which is complete for the fragments we identify. Furthermore, we prove some normal-form results.