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

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