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Symbolic dynamics is a mature yet rapidly developing area of
dynamical systems. It has established strong connections with many
areas, including linear algebra, graph theory, probability, group
theory, and the theory of computation, as well as data storage,
statistical mechanics, and $C^*$-algebras. This Second Edition
maintains the introductory character of the original 1995 edition
as a general textbook on symbolic dynamics and its applications to
coding. It is written at an elementary level and aimed at students,
well-established researchers, and experts in mathematics,
electrical engineering, and computer science. Topics are carefully
developed and motivated with many illustrative examples. There are
more than 500 exercises to test the reader's understanding. In
addition to a chapter in the First Edition on advanced topics and a
comprehensive bibliography, the Second Edition includes a detailed
Addendum, with companion bibliography, describing major
developments and new research directions since publication of the
First Edition.
Coding theory, system theory, and symbolic dynamics have much in
common. A major new theme in this area of research is that of codes
and systems based on graphical models. This volume contains survey
and research articles from leading researchers at the interface of
these subjects.
Hidden Markov processes (HMPs) are important objects of study in
many areas of pure and applied mathematics, including information
theory, probability theory, dynamical systems and statistical
physics, with applications in electrical engineering, computer
science and molecular biology. This collection of research and
survey papers presents important new results and open problems,
serving as a unifying gateway for researchers in these areas. Based
on talks given at the Banff International Research Station
Workshop, 2007, this volume addresses a central problem of the
subject: computation of the Shannon entropy rate of an HMP. This is
a key quantity in statistical physics and information theory,
characterizing the fundamental limit on compression and closely
related to channel capacity, the limit on reliable communication.
Also discussed, from a symbolic dynamics and thermodynamical
viewpoint, is the problem of characterizing the mappings between
dynamical systems which map Markov measures to Markov (or Gibbs)
measures, and which allow for Markov lifts of Markov chains.
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