Characterisation of (Sub)sequential Rational Functions over a General Class Monoids

TL;DR

This paper characterizes (sub)sequential rational functions over a broad class of monoids using a congruence relation similar to Myhill-Nerode, encompassing various algebraic structures.

Contribution

It introduces a unified algebraic framework for (sub)sequential rational functions over diverse monoids, extending existing theories.

Findings

Characterization of (sub)sequential rational functions via congruence relations.

Includes various monoids such as free monoids, groups, and tropical monoids.

Provides a general algebraic axiomatic approach.

Abstract

In this technical report we describe a general class of monoids for which (sub)sequential rational can be characterised in terms of a congruence relation in the flavour of Myhill-Nerode relation. The class of monoids that we consider can be described in terms of natural algebraic axioms, contains the free monoids, groups, the tropical monoid, and is closed under Cartesian.