ENGLISH

The Logical Approach to Automatic Sequences

By Jeffrey Shallit

Book information

Publisher
Cambridge University Press
Year
2022
ISBN
1108745245, 9781108745246
Language
english
Format
PDF
Filesize
3 MB (3326570 bytes)
Series
London Mathematical Society Lecture Note Series, 482
Pages
374\375
Topic
Mathematics Logic
Time added
2022-09-14 09:57:19

Description

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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