Published online by Cambridge University Press: 29 July 2019
The aim of this chapter is twofold. First, we recall a collection of basic mathematical notions that are needed for the discussions of the following chapters. Second, we have a first, still purely mathematical, look at the central topics of the book: languages, relations and functions between strings, as well as important operations on languages, relations and functions. We also introduce monoids, a class of algebraic structures that gives an abstract view on strings, languages, and relations.