Combinatorics Automata and Number Theory

Author: Valérie Berthé
Publisher: Cambridge University Press
ISBN: 0521515971
Format: PDF
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This series is devoted to significant topics or themes that have wide application in mathematics or mathematical science and for which a detailed development of the abstract theory is less important than a thorough and concrete exploration of the implications and applications. Books in the Encyclopedia of Mathematics and its Applications cover their subjects comprehensively. Less important results may be summarised as exercises at the ends of chapters, For technicalities, readers can be referred to the bibliography, which is expected to be comprehensive. As a result, volumes are encyclopedic references or manageable guides to major subjects.

Sequences Groups and Number Theory

Author: Valérie Berthé
Publisher: Birkhäuser
ISBN: 331969152X
Format: PDF, ePub, Docs
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This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.

Developments in Language Theory

Author: Marie-Pierre Beal
Publisher: Springer
ISBN: 3642387713
Format: PDF, Docs
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This book constitutes the proceedings of the 17th International Conference on Developments in Language Theory, DLT 2013, held in Marne-la-Vallée, France, in June 2013. The 34 full papers presented in this volume were carefully reviewed and selected from 63 submissions. The scope of the conference includes, among others, the following topics and areas: combinatorial and algebraic properties of words and languages; grammars, acceptors and transducers for strings, trees, graphs, arrays; algebraic theories for automata and languages; codes; efficient text algorithms; symbolic dynamics; decision problems; relationships to complexity theory and logic; picture description and analysis; polyominoes and bidimensional patterns; cryptography; concurrency; cellular automata; bio-inspired computing; and quantum computing.

Algebraic Informatics

Author: Traian Muntean
Publisher: Springer
ISBN: 3642406637
Format: PDF, ePub, Mobi
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This book constitutes the refereed proceedings of the 5th International Conference on Algebraic Informatics, CAI 2013, held in Porquerolles, France in September 2013. The 19 revised full papers presented together with 5 invited articles were carefully reviewed and selected from numerous submissions. The papers cover topics such as data models and coding theory; fundamental aspects of cryptography and security; algebraic and stochastic models of computing; logic and program modelling.

Formal Languages Automata and Numeration Systems 1

Author: Michel Rigo
Publisher: John Wiley & Sons
ISBN: 1119008220
Format: PDF, Kindle
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Formal Languages, Automaton and Numeration Systems presents readers with a review of research related to formal language theory, combinatorics on words or numeration systems, such as Words, DLT (Developments in Language Theory), ICALP, MFCS (Mathematical Foundation of Computer Science), Mons Theoretical Computer Science Days, Numeration, CANT (Combinatorics, Automata and Number Theory). Combinatorics on words deals with problems that can be stated in a non-commutative monoid, such as subword complexity of finite or infinite words, construction and properties of infinite words, unavoidable regularities or patterns. When considering some numeration systems, any integer can be represented as a finite word over an alphabet of digits. This simple observation leads to the study of the relationship between the arithmetical properties of the integers and the syntactical properties of the corresponding representations. One of the most profound results in this direction is given by the celebrated theorem by Cobham. Surprisingly, a recent extension of this result to complex numbers led to the famous Four Exponentials Conjecture. This is just one example of the fruitful relationship between formal language theory (including the theory of automata) and number theory.

Combinatorics Words and Symbolic Dynamics

Author: Valérie Berthé
Publisher: Cambridge University Press
ISBN: 1316462528
Format: PDF
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Internationally recognised researchers look at developing trends in combinatorics with applications in the study of words and in symbolic dynamics. They explain the important concepts, providing a clear exposition of some recent results, and emphasise the emerging connections between these different fields. Topics include combinatorics on words, pattern avoidance, graph theory, tilings and theory of computation, multidimensional subshifts, discrete dynamical systems, ergodic theory, numeration systems, dynamical arithmetics, automata theory and synchronised words, analytic combinatorics, continued fractions and probabilistic models. Each topic is presented in a way that links it to the main themes, but then they are also extended to repetitions in words, similarity relations, cellular automata, friezes and Dynkin diagrams. The book will appeal to graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, tilings and stringology. It will also interest biologists using text algorithms.