This chapter presents the main definitions and results of this book and their significance, with the help of a few basic examples. It is written so as to be readable independently of the other chapters. Definitions are sometimes given informally, with simplified notation, and most proofs are omitted. All definitions will be repeated with the necessary technical details in subsequent chapters.
In Section 1.1, we present the notion of equational set of an algebra by using as examples a context-free language, the set of cographs and the set of series-parallel graphs. We also introduce our algebraic definition of derivation trees.
In Section 1.2, we introduce the notion of recognizability in a concrete way, in terms of properties that ...