The interplay between words, computability, algebra and arithmetic has now proved its relevance and fruitfulness. Indeed, the cross-fertilization between formal logic and finite automata (such as that initiated by J.R. Büchi) or between combinatorics on words and number theory has paved the way to recent dramatic developments, for example, the transcendence results for the real numbers having a “simple” binary expansion, by B. Adamczewski and Y. Bugeaud.
This book is at the heart of this interplay through a unified exposition. Objects are considered with a perspective that comes both from theoretical computer science and mathematics. Theoretical computer science offers here topics such as decision problems and recognizability issues, whereas mathematics offers concepts such as discrete dynamical systems.
The main goal is to give a quick access, for students and researchers in mathematics or computer science, to actual research topics at the intersection between automata and formal language theory, number theory and combinatorics on words.
The first of two volumes on this subject, this book focuses on words (finite or infinite sequences of symbols, and morphic words). It can serve as a one-semester introductory course in combinatorics on words.
1. Words and Sequences from Scratch.
2. Morphic Words.
3. More Material on Infinite Words.
Michel Rigo is Professor at the Department of Mathematics at the University of Liège, Belgium.
Table of Contents
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