Submonoids and rational subsets of groups with infinitely many ends

TL;DR

This paper explores the computational complexity of membership problems in groups with infinitely many ends, showing equivalence for finitely generated submonoids and rational subsets.

Contribution

It establishes the recursive equivalence of membership problems for submonoids and rational subsets in groups with two or more ends, advancing understanding of their computational properties.

Findings

Membership problems are recursively equivalent in such groups.

The results apply to groups with two or more ends.

Provides insights into the structure of submonoids and rational subsets.

Abstract

In this paper we show that the membership problems for finitely generated submonoids and for rational subsets are recursively equivalent for groups with two or more ends.