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London Mathematical Society Lecture Note Ser.: Logical Approach to Automatic Sequences : Exploring Combinatorics on Words with Walnut by Jeffrey Shallit (2022, Trade Paperback)

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The Logical Approach to Automatic Sequences: Exploring Combinatorics on Words with Walnut (Paperback or Softback). ISBN: 9781108745246. Condition Guide. Publication Date: 9/29/2022. Item Availability.

About this product

Product Identifiers

PublisherCambridge University Press

ISBN-101108745245

ISBN-139781108745246

eBay Product ID (ePID)5057264592

Product Key Features

LanguageEnglish

Publication NameLogical Approach to Automatic Sequences : Exploring Combinatorics on Words with Walnut

SubjectGeneral

Publication Year2022

TypeTextbook

AuthorJeffrey Shallit

Subject AreaMathematics, Computers

SeriesLondon Mathematical Society Lecture Note Ser.

FormatTrade Paperback

Dimensions

Item Height0.8 in

Item Length9.1 in

Item Width5.9 in

Additional Product Features

Dewey Edition23

TitleLeadingThe

Reviews'In this book, Jeffrey Shallit gives combinatorics on words enthusiasts access to new and exciting tools to compute examples and test conjectures. Far from a mere user's manual, the text fully introduces the reader to the interactions of logic and words, proving basic theorems like the decidability of Presburger's arithmetic. It will be of great use to students and researchers, as well as the source of many future developments.' Dominique Perrin, Université Gustave Eiffel, 'This book focuses on a decision procedure, which is rather easy to implement as a computer program and allows one to prove many results, classical and new, in combinatorics on words. It addresses decision problems and enumeration problems on sequences that are expressible in first-order logic. The reader will appreciate the style, which is relaxed and pleasant to read, and the numerous examples and exercises. This book is a useful complement to the previous monograph, Automatic Sequences, co-authored by Shallit and Allouche.' Yann Bugeaud, University of Strasbourg, 'This is a marvelous book with a very fresh approach to the decidability and structural analysis of combinatorics on words. It combines three different mathematical research topics: first-order logic, automatic sequences, and combinatorics on words. More precisely, it interprets infinite morphic words as automatic sequences via k-automata and expresses properties (of words) in first-order logic. Due to the decidability of such logic, decision results and structural properties of combinatorics on words are established. A crucial role in this approach is to employ a powerful software package called Walnut. The author illustrates the power of his approach by giving a huge number of results obtained by this method. Not only are old and new results proved, but even some errors in previous ones are corrected. Anybody interested in, or curious about, this topic should be enthusiastic about this masterpiece.' Juhani Karhumäki, University of Turku (Emeritus)

Series Volume NumberSeries Number 482

IllustratedYes

Dewey Decimal511.6

Table Of Content1. Introduction; 2. Words and sequences; 3. Number representations and numeration systems; 4. Automata; 5. Automatic sequences; 6. First-order logic and automatic sequences; 7. Using Walnut; 8. First-order formulas for fundamental sequence properties; 9. Regular sequences and enumeration problems; 10. Synchronized sequences; 11. Additive number theory; 12. Paperfolding sequences; 13. A final word; References; Index.

SynopsisReaders will learn how to automatically prove or disprove new results in combinatorics and number theory in milliseconds by phrasing their desired results in first-order logic and using free software to automate the computation process. Containing more than 150 exercises, this text is an ideal resource for students and researchers., Automatic sequences are sequences over a finite alphabet generated by a finite-state machine. This book presents a novel viewpoint on automatic sequences, and more generally on combinatorics on words, by introducing a decision method through which many new results in combinatorics and number theory can be automatically proved or disproved with little or no human intervention. This approach to proving theorems is extremely powerful, allowing long and error-prone case-based arguments to be replaced by simple computations. Readers will learn how to phrase their desired results in first-order logic, using free software to automate the computation process. Results that normally require multipage proofs can emerge in milliseconds, allowing users to engage with mathematical questions that would otherwise be difficult to solve. With more than 150 exercises included, this text is an ideal resource for researchers, graduate students, and advanced undergraduates studying combinatorics, sequences, and number theory.