The Logical Approach To Automatic Sequences

Author : Jeffrey Shallit
Publisher : Cambridge University Press
ISBN 13 : 1108786979
Total Pages : 376 pages
Book Rating : 4.73/5 ( download)

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Download or read book The Logical Approach to Automatic Sequences written by Jeffrey Shallit and published by Cambridge University Press. This book was released on 2022-09-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Jean-Paul Allouche
Publisher : Cambridge University Press
ISBN 13 : 9780521823326
Total Pages : 592 pages
Book Rating : 4.23/5 ( download)

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Download or read book Automatic Sequences written by Jean-Paul Allouche and published by Cambridge University Press. This book was released on 2003-07-21 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uniting dozens of seemingly disparate results from different fields, this book combines concepts from mathematics and computer science to present the first integrated treatment of sequences generated by 'finite automata'. The authors apply the theory to the study of automatic sequences and their generalizations, such as Sturmian words and k-regular sequences. And further, they provide applications to number theory (particularly to formal power series and transcendence in finite characteristic), physics, computer graphics, and music. Starting from first principles wherever feasible, basic results from combinatorics on words, numeration systems, and models of computation are discussed. Thus this book is suitable for graduate students or advanced undergraduates, as well as for mature researchers wishing to know more about this fascinating subject. Results are presented from first principles wherever feasible, and the book is supplemented by a collection of 460 exercises, 85 open problems, and over 1600 citations to the literature.

Author : von Friedrich Haeseler
Publisher : Walter de Gruyter
ISBN 13 : 3110197960
Total Pages : 200 pages
Book Rating : 4.69/5 ( download)

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Download or read book Automatic Sequences written by von Friedrich Haeseler and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automatic sequences are sequences which are produced by a finite automaton. Although they are not random they may look as being random. They are complicated, in the sense of not being not ultimately periodic, they may look rather complicated, in the sense that it may not be easy to name the rule by which the sequence is generated, however there exists a rule which generates the sequence. The concept automatic sequences has special applications in algebra, number theory, finite automata and formal languages, combinatorics on words. The text deals with different aspects of automatic sequences, in particular: · a general introduction to automatic sequences · the basic (combinatorial) properties of automatic sequences · the algebraic approach to automatic sequences · geometric objects related to automatic sequences.

Author : Benedek Nagy
Publisher : Springer Nature
ISBN 13 : 3031402472
Total Pages : 313 pages
Book Rating : 4.70/5 ( download)

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Download or read book Implementation and Application of Automata written by Benedek Nagy and published by Springer Nature. This book was released on 2023-08-09 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 27th International Conference on Implementation and Application of Automata, CIAA 2023, held in Famagusta, North Cyprus, during September 19–22, 2023. The 20 regular papers presented in this book together with invited talks were carefully reviewed and selected from 30 submissions. The topics of the papers cover various fields in the application, implementation, and theory of automata and related structures.

Author : Thierry Lecroq
Publisher : Springer Nature
ISBN 13 : 3030850889
Total Pages : 210 pages
Book Rating : 4.83/5 ( download)

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Download or read book Combinatorics on Words written by Thierry Lecroq and published by Springer Nature. This book was released on 2021-09-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 13th International Conference on Combinatorics on Words, WORDS 2021, held virtually in September 2021. The 14 revised full papers presented in this book together with 2 invited talks were carefully reviewed and selected from 18 submissions. WORDS is the main conference series devoted to the mathematical theory of words. In particular, the combinatorial, algebraic and algorithmic aspects of words are emphasized. Motivations may also come from other domains such as theoretical computer science, bioinformatics, digital geometry, symbolic dynamics, numeration systems, text processing, number theory, etc.

Author : Anna Frid
Publisher : Springer Nature
ISBN 13 : 303133180X
Total Pages : 310 pages
Book Rating : 4.00/5 ( download)

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Download or read book Combinatorics on Words written by Anna Frid and published by Springer Nature. This book was released on 2023-05-30 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 14th International Conference on Combinatorics on Words, WORDS 2023, held in Umeå, Sweden, during June 12–16, 2023. The 19 contributed papers presented in this book were carefully reviewed and selected from 28 submissions. In addition, the volume also contains 3 invited papers. WORDS is the main conference series devoted to combinatorics on words. This area is connected to several topics from computer science and mathematics, including string algorithms, automated proofs, discrete dynamics, number theory and, of course, classical combinatorics

Author : David Gries
Publisher : Springer
ISBN 13 : 9781441928351
Total Pages : 516 pages
Book Rating : 4.59/5 ( download)

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Download or read book A Logical Approach to Discrete Math written by David Gries and published by Springer. This book was released on 2010-12-01 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here, the authors strive to change the way logic and discrete math are taught in computer science and mathematics: while many books treat logic simply as another topic of study, this one is unique in its willingness to go one step further. The book traets logic as a basic tool which may be applied in essentially every other area.

Author : Jean H. Gallier
Publisher : Courier Dover Publications
ISBN 13 : 0486780821
Total Pages : 532 pages
Book Rating : 4.25/5 ( download)

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Download or read book Logic for Computer Science written by Jean H. Gallier and published by Courier Dover Publications. This book was released on 2015-06-18 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.

Author : W. W. Youden
Publisher :
ISBN 13 :
Total Pages : 876 pages
Book Rating : 4.85/5 ( download)

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Download or read book Computer Literature Bibliography, 1946-1967 written by W. W. Youden and published by . This book was released on 1970 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : W. W. Youden
Publisher :
ISBN 13 :
Total Pages : 476 pages
Book Rating : 4.94/5 ( download)

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Download or read book Computer Literature Bibliography: 1946-1963 written by W. W. Youden and published by . This book was released on 1965 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: