Automatic Sequences : Theory, Applications, Generalizations

Combining concepts of mathematics and computer science, this book is about the sequences of symbols that can be generated by simple models of computation called ''finite automata''. Suitable for graduate students or advanced undergraduates, it starts from elementary principles and develops the basic theory. The study then progresses to show how these ideas can be applied to solve problems in number theory and physics. Uniting Dozens Of Seemingly Disparate Results From Different Fields, This Book Combines Concepts From Mathematics And Computer Science To Present The First Integrated Treatment Of Sequences Generated By 'finite Automata'. The Authors Apply The Theory To The Study Of Automatic Sequences And Their Generalizations, Such As Sturmian Words And K-regular Sequences. And Further, They Provide Applications To Number Theory (particularly To Formal Power Series And Transcendence In Finite Characteristic), Physics, Computer Graphics, And Music. Starting From First Principles Wherever Feasible, Basic Results From Combinatorics On Words, Numeration Systems, And Models Of Computation Are Discussed. Thus This Book Is Suitable For Graduate Students Or Advanced Undergraduates, As Well As For Mature Researchers Wishing To Know More About This Fascinating Subject. Results Are Presented From First Principles Wherever Feasible, And The Book Is Supplemented By A Collection Of 460 Exercises, 85 Open Problems, And Over 1600 Citations To The Literature. Jean-paul Allouche, Jeffrey Shallit. Title From Publisher's Bibliographic System (viewed On 01 Jun 2016). Mode Of Access: World Wide Web. "The authors develop the theory of automatic sequences and their generalizations, such as Sturmian words and [kappa]-regular sequences. Further, they discuss applications to number theory (particularly formal power series and transcendence in finite characteristic), physics, computer graphics, and music." "Results are presented from first principles wherever feasible, and the book is supplemented by a collection of 460 exercises, 85 open problems, and more than 1600 citations to the literature. Thus, this book is suitable for graduate students or advanced undergraduates, as well as for mature researchers wishing to know more about this subject."--Jacket This is a book about the sequences of symbols that can be generated by simple models of computation called 'finite automata'. It starts from first principles and develops the basic theory, then demonstrates applications to problems in number theory and physics. Suitable for graduates or advanced undergraduates In this chapter we introduce the basic objects of interest to this book: finite and infinite words.