The Logical Approach to Automatic Sequences

Erscheinungsjahr 2022
ISBN: 978-1-108-74524-6
Verlag: Cambridge University Press

Buch, Englisch, Band 482, 374 Seiten, Format (B × H): 150 mm x 226 mm, Gewicht: 544 g

Reihe: London Mathematical Society Lecture Note Series

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.

Autoren/Hrsg.

Shallit, Jeffrey

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker

Inhaltsverzeichnis

1. 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.

Über Autor(innen)

Shallit, Jeffrey
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.