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Jeffrey Shallit - The Logical Approach to Automatic Sequences, Häftad

Häftad, Engelska, 2022

The Logical Approach to Automatic Sequences

Exploring Combinatorics on Words with Walnut

Av Jeffrey Shallit

Del 482 i serien London Mathematical Society Lecture Note Series

1384 kr

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Beskrivning
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.
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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.

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'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

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