Systems of Word Equations and Polynomials: a New Approach

TL;DR

This paper introduces novel polynomial techniques to analyze systems of word equations, providing new bounds and insights into their structure and size dependencies.

Contribution

It presents the first nontrivial upper bounds for the sizes of systems of word equations using polynomial methods, advancing understanding in this area.

Findings

Improved bounds on system sizes of word equations

New polynomial methods for analyzing word equations

Insights into size dependencies based on independence properties

Abstract

We develop new polynomial methods for studying systems of word equations. We use them to improve some earlier results and to analyze how sizes of systems of word equations satisfying certain independence properties depend on the lengths of the equations. These methods give the first nontrivial upper bounds for the sizes of the systems.