Languages recognised by finite semigroups, and their generalisations to objects such as trees and graphs, with an emphasis on definability in monadic second-order logic

Abstract

These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond words, e.g.~infinite words, or trees or graphs. The purpose of this book is to describe the algebraic approach in a way that covers these extensions.