This survey is intended to provide an overview of one of the oldest and most celebrated
open problems in combinatorial algebra: the word problem for one-relation monoids. We …

The concept of an automaton group generalizes easily to semigroups, and the systematic
study of this area is beginning. This paper aims to contribute to that study. The basic theory …

This paper makes a comprehensive survey of results relating to finite Rees index for
semigroups. In particular, we survey of the state of knowledge on whether various finiteness …

A group is Markov if it admits a prefix-closed regular language of unique representatives
with respect to some generating set, and strongly Markov if it admits such a language of …

Automatic presentations, also called FA-presentations, were introduced to extend finite
model theory to infinite structures whilst retaining the solubility of interesting decision …

An automatic presentation for a relational structure is, informally, an abstract representation
of the elements of that structure by means of a regular language such that the relations can …

In this thesis we prove the following: The semigroup which is a disjoint union of two or three
copies of a group is a Clifford semigroup, Rees matrix semigroup or a combination between …

Automatic presentations, also called FA-presentations, were introduced to extend finite
model theory to infinite structures whilst retaining the solubility of fundamental decision …

Automatic presentations, also called FA-presentations, were introduced to extend finite
model theory to infinite structures whilst retaining the solubility of fundamental decision …

In this thesis we examine properties and constructions of graph automatic semigroups, a
generalisation of both automatic semigroups and finitely generated FA-presentable …