The Logical Approach to Automatic Sequences (Paperback)

Jeffrey Shallit

ISBN 10: 1108745245 / ISBN 13: 9781108745246

Published by Cambridge University Press, Cambridge, 2022

About this Item

Paperback. 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. Readers 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. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Seller Inventory # 9781108745246

Bibliographic Details

• Title: The Logical Approach to Automatic Sequences (Paperback)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 2022
• Language: English
• ISBN 10: 1108745245
• ISBN 13: 9781108745246
• Binding: Paperback
• Condition: new

About this title

Synopsis

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.

About the Author

Jeffrey Shallit is Professor of Computer Science in the Faculty of Mathematics at the University of Waterloo. His research areas include formal languages, finite automata, combinatorics on words, algorithmic number theory, algebra, and the history of mathematics. He has published approximately 300 articles on these topics since 1975. He is also the author or co-author of four books. He is a foreign member of the Finnish Academy of Science and Letters.