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The Logical Approach to Automatic Sequences
Jeffrey Shallit
其他書名
Exploring Combinatorics on Words with Walnut
出版Cambridge University Press, 2022-09-29
主題Computers / GeneralMathematics / CombinatoricsMathematics / Number TheoryMathematics / LogicMathematics / Discrete Mathematics
ISBN11087869799781108786973
URLhttp://books.google.com.hk/books?id=wkiJEAAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋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.