Concrete algorithms for word problem and subsemigroup problem for semigroups which are disjoint unions of finitely many copies of the free monogenic semigroup

TL;DR

This paper presents efficient algorithms for solving the word problem and membership problem in semigroups formed by finite disjoint unions of free monogenic semigroups, specifically natural numbers under addition.

Contribution

It introduces concrete algorithms that efficiently solve the word and membership problems for a specific class of semigroups formed by disjoint unions of free monogenic semigroups.

Findings

Soluble word problem for these semigroups

Soluble membership problem for these semigroups

Efficient algorithms provided

Abstract

Every semigroup which is a finite disjoint union of copies of the free mono- genic semigroup (natural numbers under addition) has soluble word prob- lem and soluble membership problem. Efficient algorithms are given for both problems.