Profinite Semigroups and Symbolic Dynamics
Profinite Semigroups and Symbolic Dynamics

Author: Jorge Almeida

Publisher: Springer Nature

Published: 2020-09-10

Total Pages: 278

ISBN-13: 3030552152

DOWNLOAD EBOOK

This book describes the relation between profinite semigroups and symbolic dynamics. Profinite semigroups are topological semigroups which are compact and residually finite. In particular, free profinite semigroups can be seen as the completion of free semigroups with respect to the profinite metric. In this metric, two words are close if one needs a morphism on a large finite monoid to distinguish them. The main focus is on a natural correspondence between minimal shift spaces (closed shift-invariant sets of two-sided infinite words) and maximal J-classes (certain subsets of free profinite semigroups). This correspondence sheds light on many aspects of both profinite semigroups and symbolic dynamics. For example, the return words to a given word in a shift space can be related to the generators of the group of the corresponding J-class. The book is aimed at researchers and graduate students in mathematics or theoretical computer science.

Dimension Groups and Dynamical Systems
Dimension Groups and Dynamical Systems

Author: Fabien Durand

Publisher: Cambridge University Press

Published: 2022-02-03

Total Pages: 594

ISBN-13: 1108986099

DOWNLOAD EBOOK

This book is the first self-contained exposition of the fascinating link between dynamical systems and dimension groups. The authors explore the rich interplay between topological properties of dynamical systems and the algebraic structures associated with them, with an emphasis on symbolic systems, particularly substitution systems. It is recommended for anybody with an interest in topological and symbolic dynamics, automata theory or combinatorics on words. Intended to serve as an introduction for graduate students and other newcomers to the field as well as a reference for established researchers, the book includes a thorough account of the background notions as well as detailed exposition – with full proofs – of the major results of the subject. A wealth of examples and exercises, with solutions, serve to build intuition, while the many open problems collected at the end provide jumping-off points for future research.

An Introduction to Symbolic Dynamics and Coding
An Introduction to Symbolic Dynamics and Coding

Author: Douglas Lind

Publisher: Cambridge University Press

Published: 2021-01-21

Total Pages: 571

ISBN-13: 110882028X

DOWNLOAD EBOOK

Elementary introduction to symbolic dynamics, updated to describe the main advances in the subject since the original publication in 1995.

Topological Duality for Distributive Lattices
Topological Duality for Distributive Lattices

Author: Mai Gehrke

Publisher: Cambridge University Press

Published: 2024-02-29

Total Pages: 370

ISBN-13: 1009349716

DOWNLOAD EBOOK

Introducing Stone–Priestley duality theory and its applications to logic and theoretical computer science, this book equips graduate students and researchers with the theoretical background necessary for reading and understanding current research in the area. After giving a thorough introduction to the algebraic, topological, logical, and categorical aspects of the theory, the book covers two advanced applications in computer science, namely in domain theory and automata theory. These topics are at the forefront of active research seeking to unify semantic methods with more algorithmic topics in finite model theory. Frequent exercises punctuate the text, with hints and references provided.

Symbolic Dynamics and its Applications
Symbolic Dynamics and its Applications

Author: Peter Walters

Publisher: American Mathematical Soc.

Published: 1992

Total Pages: 472

ISBN-13: 0821851462

DOWNLOAD EBOOK

This volume contains the proceedings of the conference, Symbolic Dynamics and its Applications, held at Yale University in the summer of 1991 in honour of Roy L. Adler on his sixtieth birthday. The conference focused on symbolic dynamics and its applications to other fields, including: ergodic theory, smooth dynamical systems, information theory, automata theory, and statistical mechanics. Featuring a range of contributions from some of the leaders in the field, this volume presents an excellent overview of the subject.

Topics in Symbolic Dynamics and Applications
Topics in Symbolic Dynamics and Applications

Author: F. Blanchard

Publisher: Cambridge University Press

Published: 2000-06-29

Total Pages: 268

ISBN-13: 9780521796606

DOWNLOAD EBOOK

This book is devoted to recent developments in symbolic dynamics, and it comprises eight chapters. The first two are concerned with the study of symbolic sequences of 'low complexity', the following two introduce 'high complexity' systems. The later chapters go on to deal with more specialised topics including ergodic theory, number theory, and one-dimensional dynamics.

125 Problems in Text Algorithms
125 Problems in Text Algorithms

Author: Maxime Crochemore

Publisher: Cambridge University Press

Published: 2021-07

Total Pages: 345

ISBN-13: 110883583X

DOWNLOAD EBOOK

Worked problems offer an interesting way to learn and practice with key concepts of string algorithms and combinatorics on words.

Symbolic Dynamics and its Applications
Symbolic Dynamics and its Applications

Author: Susan G. Williams

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 168

ISBN-13: 0821831577

DOWNLOAD EBOOK

Symbolic dynamics originated as a tool for analyzing dynamical systems and flows by discretizing space as well as time. The development of information theory gave impetus to the study of symbol sequences as objects in their own right. Today, symbolic dynamics has expanded to encompass multi-dimensional arrays of symbols and has found diverse applications both within and beyond mathematics. This volume is based on the AMS Short Course on Symbolic Dynamics and its Applications. It contains introductory articles on the fundamental ideas of the field and on some of its applications. Topics include the use of symbolic dynamics techniques in coding theory and in complex dynamics, the relation between the theory of multi-dimensional systems and the dynamics of tilings, and strong shift equivalence theory. Contributors to the volume are experts in the field and are clear expositors. The book is suitable for graduate students and research mathematicians interested in symbolic dynamics and its applications.