„This book follows [Formal languages, automata and numeration systems. Vol. 1. Introduction to combinatorics on words. Hoboken, NJ: John Wiley& Sons; London: ISTE (2014; Zbl 6384340)]. It contains essentially two parts that are quite interesting.“ (Zentralblatt MATH 2016)This book follows [Formal languages, automata and numeration systems. Vol. 1. Introduc-tion to combinatorics on words. Hoboken, NJ: John Wiley& Sons; London: ISTE (2014; Zbl 6384340)]. It contains essentially two parts that are quite interesting.

Formal Languages, Automata and Numeration Systems 2

Applications to Recognizability and Decidability

von Michel Rigo

The interplay between words, computability, algebra andarithmetic 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 betweencombinatorics on words and number theory has paved the way torecent dramatic developments, for example, the transcendenceresults for the real numbers having a „simple“ binaryexpansion, by B. Adamczewski and Y. Bugeaud. This book is at the heart of this interplay through a unifiedexposition. Objects are considered with a perspective that comesboth from theoretical computer science and mathematics. Theoreticalcomputer science offers here topics such as decision problems andrecognizability issues, whereas mathematics offers concepts such asdiscrete dynamical systems. The main goal is to give a quick access, for students andresearchers in mathematics or computer science, to actual researchtopics at the intersection between automata and formal languagetheory, number theory and combinatorics on words. The second of two volumes on this subject, this book coversregular languages, numeration systems, formal methods applied todecidability issues about infinite words and sets of numbers.