Automatic sets of rational numbers

TL;DR

This paper introduces the concept of k-automatic sets of rational numbers, extending the well-studied integer case, and explores their fundamental properties such as closure and decidability.

Contribution

It develops the theory of k-automatic sets of rational numbers, establishing foundational properties and decidability results that were not previously known.

Findings

Established closure properties of k-automatic rational sets

Proved decidability of key problems for these sets

Extended the theory from integers to rationals

Abstract

The notion of a k-automatic set of integers is well-studied. We develop a new notion - the k-automatic set of rational numbers - and prove basic properties of these sets, including closure properties and decidability.