A Language Hierarchy of Binary Relations
Tara Brough, Alan J. Cain

TL;DR
This paper investigates a hierarchy of binary relations on words, classifying them based on language classes and perspectives, with applications to monoid word problems.
Contribution
It introduces a new hierarchy of binary relation classes on words, linked to language classes and monoid word problems, providing a structured framework.
Findings
Established a hierarchy of relation classes
Provided examples distinguishing classes
Connected relation classes to monoid word problems
Abstract
Motivated by the study of word problems of monoids, we explore two ways of viewing binary relations on as languages. We exhibit a hierarchy of classes of binary relations on , according to the class of languages the relation belongs to and the chosen viewpoint. We give examples of word problems of monoids distinguishing the various classes.
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