The Logical Approach To Automatic Sequences
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| Author | : Jeffrey Shallit |
| Publisher | : Cambridge University Press |
| Total Pages | : 376 |
| Release | : 2022-09-30 |
| Genre | : Computers |
| ISBN | : 1108786979 |
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 |
| Total Pages | : 592 |
| Release | : 2003-07-21 |
| Genre | : Computers |
| ISBN | : 9780521823326 |
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 | : Benedek Nagy |
| Publisher | : Springer Nature |
| Total Pages | : 313 |
| Release | : 2023-08-09 |
| Genre | : Computers |
| ISBN | : 3031402472 |
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 |
| Total Pages | : 210 |
| Release | : 2021-09-06 |
| Genre | : Mathematics |
| ISBN | : 3030850889 |
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 |
| Total Pages | : 310 |
| Release | : 2023-05-30 |
| Genre | : Mathematics |
| ISBN | : 303133180X |
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 | : Venanzio Capretta |
| Publisher | : Springer Nature |
| Total Pages | : 284 |
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| Genre | : |
| ISBN | : 3031617169 |
| Author | : Szilárd Zsolt Fazekas |
| Publisher | : Springer Nature |
| Total Pages | : 379 |
| Release | : |
| Genre | : |
| ISBN | : 3031711122 |
| Author | : Christoph Benzmüller |
| Publisher | : Springer Nature |
| Total Pages | : 493 |
| Release | : |
| Genre | : |
| ISBN | : 3031634985 |
| Author | : Ludovic Levy Patey |
| Publisher | : Springer Nature |
| Total Pages | : 490 |
| Release | : |
| Genre | : |
| ISBN | : 3031643097 |
| Author | : Jean H. Gallier |
| Publisher | : Courier Dover Publications |
| Total Pages | : 532 |
| Release | : 2015-06-18 |
| Genre | : Mathematics |
| ISBN | : 0486780821 |
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.
