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题名/责任者:

The logical approach to automatic sequences : exploring combinatorics on words with walnut / Jeffrey Shallit

出版发行项:

Cambridge : Cambridge University Press, 2023

ISBN:

9781108745246 (paperback)

载体形态项:

xv, 358 pages ; 23 cm

丛编说明:

London Mathematical Society lecture note series ; 482

个人责任者:

Shallit, Jeffrey Outlaw, author

论题主题:

Combinatorial analysis-Data processing

中图法分类号:

O157.1

书目附注:

Includes bibliographical references and index.

摘要附注:

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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