Algebraic Theory Of Automata
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Algebraic Theory Of Automata
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Author : Abraham Ginzburg
language : en
Publisher: Academic Press
Release Date : 2014-06-25
Algebraic Theory Of Automata written by Abraham Ginzburg and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-25 with Technology & Engineering categories.
Algebraic Theory of Automata provides information pertinent to the methods and results of algebraic theory of automata. This book covers a variety of topics, including sets, semigroup, groupoids, isomorphism, semiautomata, proof of Kleene's theorem, and algebraic manipulations. Organized into seven chapters, this book begins with an overview of the fundamental properties of groups and semigroups. This text then examines the notion of semiautomaton, which serves as a basis for a rich and interesting theory. Other chapters consider algebraic notions and methods that are very useful in dealing with semiautomata. This book discusses as well some properties of the notion of covering of semiautomata. The final chapter deals with the theory of Krohn and Rhodes. This book is a valuable resource for graduate students.
Algebraic Theory Of Automata And Languages
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Author : Masami It?
language : en
Publisher: World Scientific
Release Date : 2004
Algebraic Theory Of Automata And Languages written by Masami It? and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Although there are some books dealing with algebraic theory of automata, their contents consist mainly of Krohn-Rhodes theory and related topics. The topics in the present book are rather different. For example, automorphism groups of automata and the partially ordered sets of automata are systematically discussed. Moreover, some operations on languages and special classes of regular languages associated with deterministic and nondeterministic directable automata are dealt with. The book is self-contained and hence does not require any knowledge of automata and formal languages.
Algebraic Theory Of Automata Networks
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Author : Pal Domosi
language : en
Publisher: SIAM
Release Date : 2005-01-01
Algebraic Theory Of Automata Networks written by Pal Domosi and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
Investigates automata networks as algebraic structures and develops their theory in line with other algebraic theories, such as those of semigroups, groups, rings, and fields. The authors also investigate automata networks as products of automata, that is, as compositions of automata obtained by cascading without feedback or with feedback of various restricted types or, most generally, with the feedback dependencies controlled by an arbitrary directed graph. They survey and extend the fundamental results in regard to automata networks, including the main decomposition theorems of Letichevsky, of Krohn and Rhodes, and of others.
Applications Of Automata Theory And Algebra
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Author : John L. Rhodes
language : en
Publisher: World Scientific
Release Date : 2010
Applications Of Automata Theory And Algebra written by John L. Rhodes and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
This book was originally written in 1969 by Berkeley mathematician John Rhodes. It is the founding work in what is now called algebraic engineering, an emerging field created by using the unifying scheme of finite state machine models and their complexity to tie together many fields: finite group theory, semigroup theory, automata and sequential machine theory, finite phase space physics, metabolic and evolutionary biology, epistemology, mathematical theory of psychoanalysis, philosophy, and game theory. The author thus introduced a completely original algebraic approach to complexity and the understanding of finite systems. The unpublished manuscript, often referred to as "The Wild Book," became an underground classic, continually requested in manuscript form, and read by many leading researchers in mathematics, complex systems, artificial intelligence, and systems biology. Yet it has never been available in print until now. This first published edition has been edited and updated by Chrystopher Nehaniv for the 21st century. Its novel and rigorous development of the mathematical theory of complexity via algebraic automata theory reveals deep and unexpected connections between algebra (semigroups) and areas of science and engineering. Co-founded by John Rhodes and Kenneth Krohn in 1962, algebraic automata theory has grown into a vibrant area of research, including the complexity of automata, and semigroups and machines from an algebraic viewpoint, and which also touches on infinite groups, and other areas of algebra. This book sets the stage for the application of algebraic automata theory to areas outside mathematics. The material and references have been brought up to date bythe editor as much as possible, yet the book retains its distinct character and the bold yet rigorous style of the author. Included are treatments of topics such as models of time as algebra via semigroup theory; evolution-complexity relations applicable to both ontogeny and evolution; an approach to classification of biological reactions and pathways; the relationships among coordinate systems, symmetry, and conservation principles in physics; discussion of "punctuated equilibrium" (prior to Stephen Jay Gould); games; and applications to psychology, psychoanalysis, epistemology, and the purpose of life. The approach and contents will be of interest to a variety of researchers and students in algebra as well as to the diverse, growing areas of applications of algebra in science and engineering. Moreover, many parts of the book will be intelligible to non-mathematicians, including students and experts from diverse backgrounds.
Algebraic Theory Of Automata And Languages
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Author : Masami Ito
language : en
Publisher: World Scientific
Release Date : 2004
Algebraic Theory Of Automata And Languages written by Masami Ito and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computers categories.
Although there are some books dealing with algebraic theory ofautomata, their contents consist mainly of KrohnOCoRhodes theory andrelated topics. The topics in the present book are ratherdifferent. For example, automorphism groups of automata and thepartially ordered sets of automata are systematicallydiscussed. Moreover, some operations on languages and special classesof regular languages associated with deterministic andnondeterministic directable automata are dealt with. The book isself-contained and hence does not require any knowledge of automataand formal languages."
Elements Of Automata Theory
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Author : Jacques Sakarovitch
language : en
Publisher: Cambridge University Press
Release Date : 2009-10-01
Elements Of Automata Theory written by Jacques Sakarovitch and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-01 with Mathematics categories.
Automata theory lies at the foundation of computer science, and is vital to a theoretical understanding of how computers work and what constitutes formal methods. This treatise gives a rigorous account of the topic and illuminates its real meaning by looking at the subject in a variety of ways. The first part of the book is organised around notions of rationality and recognisability. The second part deals with relations between words realised by finite automata, which not only exemplifies the automata theory but also illustrates the variety of its methods and its fields of application. Many exercises are included, ranging from those that test the reader, to those that are technical results, to those that extend ideas presented in the text. Solutions or answers to many of these are included in the book.
Applied Automata Theory
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Author : Julius T. Tou
language : en
Publisher: Academic Press
Release Date : 2013-10-22
Applied Automata Theory written by Julius T. Tou and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Technology & Engineering categories.
Applied Automata Theory provides an engineering style of presentation of some of the applied work in the field of automata theory. Topics covered range from algebraic foundations and recursive functions to regular expressions, threshold logic, and switching circuits. Coding problems and stochastic processes are also discussed, along with content addressable memories, probabilistic reliability, and Turing machines. Much emphasis is placed on engineering applications. Comprised of nine chapters, this book first deals with the algebraic foundations of automata theory, focusing on concepts such as semigroups, groups and homomorphisms, and partially ordered sets and lattices, as well as congruences and other relations. The reader is then introduced to regular expressions; stochastic automata and discrete systems theory; and switching networks as models of discrete stochastic processes. Subsequent chapters explore applications of automata theory in coding; content addressable and distributed logic memories; recursive functions and switching-circuit theory; and synthesis of a cellular computer. The book concludes with an assessment of the fundamentals of threshold logic. This monograph is intended for graduates or advanced undergraduates taking a course in information science or a course on discrete systems in modern engineering curriculum.
Automata Theory With Modern Applications
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Author : James A. Anderson
language : en
Publisher: Cambridge University Press
Release Date : 2006-06-22
Automata Theory With Modern Applications written by James A. Anderson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-22 with Mathematics categories.
Recent applications to biomolecular science and DNA computing have created a new audience for automata theory and formal languages. This is the only introductory book to cover such applications. It begins with a clear and readily understood exposition of the fundamentals that assumes only a background in discrete mathematics. The first five chapters give a gentle but rigorous coverage of basic ideas as well as topics not found in other texts at this level, including codes, retracts and semiretracts. Chapter 6 introduces combinatorics on words and uses it to describe a visually inspired approach to languages. The final chapter explains recently-developed language theory coming from developments in bioscience and DNA computing. With over 350 exercises (for which solutions are available), many examples and illustrations, this text will make an ideal contemporary introduction for students; others, new to the field, will welcome it for self-learning.
Discrete Algebraic Methods
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Author : Volker Diekert
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-05-24
Discrete Algebraic Methods written by Volker Diekert and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-24 with Mathematics categories.
The idea behind this book is to provide the mathematical foundations for assessing modern developments in the Information Age. It deepens and complements the basic concepts, but it also considers instructive and more advanced topics. The treatise starts with a general chapter on algebraic structures; this part provides all the necessary knowledge for the rest of the book. The next chapter gives a concise overview of cryptography. Chapter 3 on number theoretic algorithms is important for developping cryptosystems, Chapter 4 presents the deterministic primality test of Agrawal, Kayal, and Saxena. The account to elliptic curves again focuses on cryptographic applications and algorithms. With combinatorics on words and automata theory, the reader is introduced to two areas of theoretical computer science where semigroups play a fundamental role.The last chapter is devoted to combinatorial group theory and its connections to automata. Contents: Algebraic structures Cryptography Number theoretic algorithms Polynomial time primality test Elliptic curves Combinatorics on words Automata Discrete infinite groups