The Logical Approach to Automatic Sequences

The Logical Approach to Automatic Sequences PDF Author: Jeffrey Shallit
Publisher: Cambridge University Press
ISBN: 1108786979
Category : Computers
Languages : en
Pages : 376

Book 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.

Automatic Sequences

Automatic Sequences PDF Author: Jean-Paul Allouche
Publisher: Cambridge University Press
ISBN: 9780521823326
Category : Computers
Languages : en
Pages : 592

Book Description
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.

Combinatorics on Words

Combinatorics on Words PDF Author: Thierry Lecroq
Publisher: Springer Nature
ISBN: 3030850889
Category : Mathematics
Languages : en
Pages : 210

Book Description
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.

Logic for Computer Science

Logic for Computer Science PDF Author: Jean H. Gallier
Publisher: Courier Dover Publications
ISBN: 0486780821
Category : Mathematics
Languages : en
Pages : 532

Book Description
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.

Combinatorics on Words

Combinatorics on Words PDF Author: Anna Frid
Publisher: Springer Nature
ISBN: 303133180X
Category : Mathematics
Languages : en
Pages : 310

Book Description
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

Implementation and Application of Automata

Implementation and Application of Automata PDF Author: Benedek Nagy
Publisher: Springer Nature
ISBN: 3031402472
Category : Computers
Languages : en
Pages : 313

Book Description
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.

A Second Course in Formal Languages and Automata Theory

A Second Course in Formal Languages and Automata Theory PDF Author: Jeffrey Shallit
Publisher: Cambridge University Press
ISBN: 0521865727
Category : Computers
Languages : en
Pages : 0

Book Description
A textbook for a graduate course on formal languages and automata theory, building on prior knowledge of theoretical computer models.

Jewels Of Stringology: Text Algorithms

Jewels Of Stringology: Text Algorithms PDF Author: Maxime Crochemore
Publisher: World Scientific
ISBN: 9814489875
Category : Computers
Languages : en
Pages : 322

Book Description
The term “stringology” is a popular nickname for text algorithms, or algorithms on strings. This book deals with the most basic algorithms in the area. Most of them can be viewed as “algorithmic jewels” and deserve reader-friendly presentation. One of the main aims of the book is to present several of the most celebrated algorithms in a simple way by omitting obscuring details and separating algorithmic structure from combinatorial theoretical background. The book reflects the relationships between applications of text-algorithmic techniques and the classification of algorithms according to the measures of complexity considered. The text can be viewed as a parade of algorithms in which the main purpose is to discuss the foundations of the algorithms and their interconnections. One can partition the algorithmic problems discussed into practical and theoretical problems. Certainly, string matching and data compression are in the former class, while most problems related to symmetries and repetitions in texts are in the latter. However, all the problems are interesting from an algorithmic point of view and enable the reader to appreciate the importance of combinatorics on words as a tool in the design of efficient text algorithms.In most textbooks on algorithms and data structures, the presentation of efficient algorithms on words is quite short as compared to issues in graph theory, sorting, searching, and some other areas. At the same time, there are many presentations of interesting algorithms on words accessible only in journals and in a form directed mainly at specialists. This book fills the gap in the book literature on algorithms on words, and brings together the many results presently dispersed in the masses of journal articles. The presentation is reader-friendly; many examples and about two hundred figures illustrate nicely the behaviour of otherwise very complex algorithms.
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