Profinite Semigroups And Symbolic Dynamics
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Profinite Semigroups and Symbolic Dynamics
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.
Structural Theory of Automata, Semigroups, and Universal Algebra
Author: Valery B. Kudryavtsev
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-01-18
Several of the contributions to this volume bring forward many mutually beneficial interactions and connections between the three domains of the title. Developing them was the main purpose of the NATO ASI summerschool held in Montreal in 2003. Although some connections, for example between semigroups and automata, were known for a long time, developing them and surveying them in one volume is novel and hopefully stimulating for the future. Another aspect is the emphasis on the structural theory of automata that studies ways to contstruct big automata from small ones. The volume also has contributions on top current research or surveys in the three domains. One contribution even links clones of universal algebra with the computational complexity of computer science. Three contributions introduce the reader to research in the former East block.
An Introduction to Symbolic Dynamics and Coding
Author: Douglas A. Lind
language: en
Publisher: Cambridge University Press
Release Date: 2021-01-21
Elementary introduction to symbolic dynamics, updated to describe the main advances in the subject since the original publication in 1995.