The termination of Nielsen transformations applied to word equations with length constraints

Fuente: arXiv
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Main Authors: Przybocki, Benjamin, Barrett, Clark
Format: Preprint
Published: 2025
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author Przybocki, Benjamin
Barrett, Clark
author_facet Przybocki, Benjamin
Barrett, Clark
contents Nielsen transformations form the basis of a simple and widely used procedure for solving word equations. We make progress on the problem of determining when this procedure terminates in the presence of length constraints. To do this, we introduce extended word equations, a mathematical model of a word equation with partial information about length constraints. We then define extended Nielsen transformations, which adapt Nielsen transformations to the setting of extended word equations. We provide a partial characterization of when repeatedly applying extended Nielsen transformations to an extended word equation is guaranteed to terminate.
format Preprint
id arxiv_https___arxiv_org_abs_2501_11789
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The termination of Nielsen transformations applied to word equations with length constraints
Przybocki, Benjamin
Barrett, Clark
Logic in Computer Science
Formal Languages and Automata Theory
Nielsen transformations form the basis of a simple and widely used procedure for solving word equations. We make progress on the problem of determining when this procedure terminates in the presence of length constraints. To do this, we introduce extended word equations, a mathematical model of a word equation with partial information about length constraints. We then define extended Nielsen transformations, which adapt Nielsen transformations to the setting of extended word equations. We provide a partial characterization of when repeatedly applying extended Nielsen transformations to an extended word equation is guaranteed to terminate.
title The termination of Nielsen transformations applied to word equations with length constraints
topic Logic in Computer Science
Formal Languages and Automata Theory
url https://arxiv.org/abs/2501.11789