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- 000 02002nam a2200289Ii 4500
- 008 190430s2023 enk b 001 0 eng d
- 020 __ |a 9781108745246 (paperback)
- 020 __ |z 9781108775267 (ebook)
- 040 __ |a UkCbUP |b eng |e rda |c UkCbUP
- 050 _4 |a QA164 |b .S32 2023
- 100 1_ |a Shallit, Jeffrey Outlaw, |e author
- 245 14 |a The logical approach to automatic sequences : |b exploring combinatorics on words with walnut / |c Jeffrey Shallit
- 260 __ |a Cambridge : |b Cambridge University Press, |c 2023
- 300 __ |a xv, 358 pages ; |c 23 cm
- 336 __ |a text |b txt |2 rdacontent
- 337 __ |a unmediated |b n |2 rdamedia
- 338 __ |a volume |b nc |2 rdacarrier
- 490 1_ |a London Mathematical Society lecture note series ; |v 482
- 504 __ |a Includes bibliographical references and index.
- 520 __ |a 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
- 650 _0 |a Combinatorial analysis |x Data processing