Algebraic Automata Theory

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Applications of Automata Theory and Algebra

Author : John L. Rhodes
Publisher : World Scientific
ISBN 13 : 9812836969
Total Pages : 293 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Applications of Automata Theory and Algebra by : John L. Rhodes

Download or read book Applications of Automata Theory and Algebra written by John L. Rhodes and published by World Scientific. This book was released on 2010 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 The unpublished manuscript, often referred to as "The Wild Book," became an underground classic, continually requested in manuscript form, and read by many leading researchers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

Author : Masami It?
Publisher : World Scientific
ISBN 13 : 9810247273
Total Pages : 210 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Algebraic Theory of Automata and Languages by : Masami It?

Download or read book Algebraic Theory of Automata and Languages written by Masami It? and published by World Scientific. This book was released on 2004 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Automata Theory

Author : M. Holcombe
Publisher : Cambridge University Press
ISBN 13 : 9780521604925
Total Pages : 248 pages
Book Rating : 4.6/5 (49 download)

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Book Synopsis Algebraic Automata Theory by : M. Holcombe

Download or read book Algebraic Automata Theory written by M. Holcombe and published by Cambridge University Press. This book was released on 2004-06-03 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Original publisher: Washington, DC: U.S. Dept. of Transportation, Federal Aviation Administration, Office of Aerospace Medicine, 2003] OCLC Number: (OCoLC)74267777 Subject: Airplanes -- Cockpits. Excerpt: ... -9 +-5; * /- (-8 89 @ 9 @ 2: BGH9 @ > BD9D; 9 @: > C9 D2 D286 ? 7 @: 8 2CC: CD2 > 46 D? 4? = @ D6B7246 D2C; C # &-? I 1.94 * 7 + 492 > 86 D? ., 0 = 2 @ 5: C @ ? + B6 =? F6 9: 89 2 86 = 2 @ 5: C @ ? BD9 " E @ D? DB24; " E @ * 6 = 3?; 9 + C6 5 ? F6B * 9; + 05 / + C6D -/ 1 D?: > D6B46 @ D 2CC: 8 > 65 B25: 2 C6BD 2CC: 8 > 65: > D6BC64D: ? > > D? 7 7? B 9? 8 @ B? 465EB6 *: -; 03, + C6 65 ? ED3? E > 5 B25: 2 8 @ B? 465EB6 * 03,15 + C6D: > 3? E > 5 B25: 2 4: > 8 * 3, * 77 + D6B D96 2 2D6 2: B @? BD: > D? D96 7 * 3, * 77 + 2D6 2: B @? BD # of levels within Flight Task showed that the last four tasks Figure 9 shows the root-mean-square cross-track error, were judged to have produced significantly higher workload by display type, for three flight segments. The inbound than the first three tasks, t ( 15...

Algebraic Theory of Automata Networks

Author : Pal Domosi
Publisher : SIAM
ISBN 13 : 9780898718492
Total Pages : 270 pages
Book Rating : 4.7/5 (184 download)

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Book Synopsis Algebraic Theory of Automata Networks by : Pal Domosi

Download or read book Algebraic Theory of Automata Networks written by Pal Domosi and published by SIAM. This book was released on 2005-01-01 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Theory of Automata

Author : Abraham Ginzburg
Publisher : Academic Press
ISBN 13 : 148322516X
Total Pages : 176 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Algebraic Theory of Automata by : Abraham Ginzburg

Download or read book Algebraic Theory of Automata written by Abraham Ginzburg and published by Academic Press. This book was released on 2014-06-25 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Theories

Author : E.G. Manes
Publisher : Springer Science & Business Media
ISBN 13 : 1461298601
Total Pages : 364 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Algebraic Theories by : E.G. Manes

Download or read book Algebraic Theories written by E.G. Manes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past decade, category theory has widened its scope and now inter acts with many areas of mathematics. This book develops some of the interactions between universal algebra and category theory as well as some of the resulting applications. We begin with an exposition of equationally defineable classes from the point of view of "algebraic theories," but without the use of category theory. This serves to motivate the general treatment of algebraic theories in a category, which is the central concern of the book. (No category theory is presumed; rather, an independent treatment is provided by the second chap ter.) Applications abound throughout the text and exercises and in the final chapter in which we pursue problems originating in topological dynamics and in automata theory. This book is a natural outgrowth of the ideas of a small group of mathe maticians, many of whom were in residence at the Forschungsinstitut für Mathematik of the Eidgenössische Technische Hochschule in Zürich, Switzerland during the academic year 1966-67. It was in this stimulating atmosphere that the author wrote his doctoral dissertation. The "Zürich School," then, was Michael Barr, Jon Beck, John Gray, Bill Lawvere, Fred Linton, and Myles Tierney (who were there) and (at least) Harry Appelgate, Sammy Eilenberg, John Isbell, and Saunders Mac Lane (whose spiritual presence was tangible.) I am grateful to the National Science Foundation who provided support, under grants GJ 35759 and OCR 72-03733 A01, while I wrote this book.

Elements of Automata Theory

Author : Jacques Sakarovitch
Publisher : Cambridge University Press
ISBN 13 : 1139643797
Total Pages : 818 pages
Book Rating : 4.1/5 (396 download)

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Book Synopsis Elements of Automata Theory by : Jacques Sakarovitch

Download or read book Elements of Automata Theory written by Jacques Sakarovitch and published by Cambridge University Press. This book was released on 2009-10-01 with total page 818 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Finite Automata, Their Algebras and Grammars

Author : J. Richard Büchi
Publisher : Springer Science & Business Media
ISBN 13 : 1461388538
Total Pages : 335 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Finite Automata, Their Algebras and Grammars by : J. Richard Büchi

Download or read book Finite Automata, Their Algebras and Grammars written by J. Richard Büchi and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author, who died in 1984, is well-known both as a person and through his research in mathematical logic and theoretical computer science. In the first part of the book he presents the new classical theory of finite automata as unary algebras which he himself invented about 30 years ago. Many results, like his work on structure lattices or his characterization of regular sets by generalized regular rules, are unknown to a wider audience. In the second part of the book he extends the theory to general (non-unary, many-sorted) algebras, term rewriting systems, tree automata, and pushdown automata. Essentially Büchi worked independent of other rersearch, following a novel and stimulating approach. He aimed for a mathematical theory of terms, but could not finish the book. Many of the results are known by now, but to work further along this line presents a challenging research program on the borderline between universal algebra, term rewriting systems, and automata theory. For the whole book and again within each chapter the author starts at an elementary level, giving careful explanations and numerous examples and exercises, and then leads up to the research level. In this way he covers the basic theory as well as many nonstandard subjects. Thus the book serves as a textbook for both the beginner and the advances student, and also as a rich source for the expert.

Discrete Algebraic Methods

Author : Volker Diekert
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110416328
Total Pages : 424 pages
Book Rating : 4.1/5 (14 download)

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Book Synopsis Discrete Algebraic Methods by : Volker Diekert

Download or read book Discrete Algebraic Methods written by Volker Diekert and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-05-24 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Noncommutative Rational Series with Applications

Author : Jean Berstel
Publisher : Cambridge University Press
ISBN 13 : 0521190223
Total Pages : 263 pages
Book Rating : 4.5/5 (211 download)

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Book Synopsis Noncommutative Rational Series with Applications by : Jean Berstel

Download or read book Noncommutative Rational Series with Applications written by Jean Berstel and published by Cambridge University Press. This book was released on 2011 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern account of the subject and its applications. Excellent resource for those working in algebra and theoretical computer science.

Automata Theory with Modern Applications

Author : James A. Anderson
Publisher : Cambridge University Press
ISBN 13 : 1139458213
Total Pages : 3 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Automata Theory with Modern Applications by : James A. Anderson

Download or read book Automata Theory with Modern Applications written by James A. Anderson and published by Cambridge University Press. This book was released on 2006-06-22 with total page 3 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Codes and Automata

Author : Jean Berstel
Publisher : Cambridge University Press
ISBN 13 : 052188831X
Total Pages : 634 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Codes and Automata by : Jean Berstel

Download or read book Codes and Automata written by Jean Berstel and published by Cambridge University Press. This book was released on 2010 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This major revision of Berstel and Perrin's classic Theory of Codes has been rewritten with a more modern focus and a much broader coverage of the subject. The concept of unambiguous automata, which is intimately linked with that of codes, now plays a significant role throughout the book, reflecting developments of the last 20 years. This is complemented by a discussion of the connection between codes and automata, and new material from the field of symbolic dynamics. The authors have also explored links with more practical applications, including data compression and cryptography. The treatment remains self-contained: there is background material on discrete mathematics, algebra and theoretical computer science. The wealth of exercises and examples make it ideal for self-study or courses. In summary, this is a comprehensive reference on the theory of variable-length codes and their relation to automata.

Semirings, Automata, Languages

Author : W. Kuich
Publisher : Springer Science & Business Media
ISBN 13 : 3642699596
Total Pages : 382 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Semirings, Automata, Languages by : W. Kuich

Download or read book Semirings, Automata, Languages written by W. Kuich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automata theory is the oldest among the disciplines constituting the subject matter of this Monograph Series: theoretical computer science. Indeed, automata theory and the closely related theory of formal languages form nowadays such a highly developed and diversified body of knowledge that even an exposition of "reasonably important" results is not possible within one volume. The purpose of this book is to develop the theory of automata and formal languages, starting from ideas based on linear algebra. By what was said above, it should be obvious that we do not intend to be encyclopedic. However, this book contains the basics of regular and context-free languages (including some new results), as well as a rather complete theory of pushdown automata and variations (e. g. counter automata). The wellknown AFL theory is extended to power series ("AFP theory"). Additional new results include, for instance, a grammatical characterization of the cones and the principal cones of context-free languages, as well as new decidability results.

Applied Automata Theory

Author : Julius T. Tou
Publisher : Academic Press
ISBN 13 : 1483225194
Total Pages : 343 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Applied Automata Theory by : Julius T. Tou

Download or read book Applied Automata Theory written by Julius T. Tou and published by Academic Press. This book was released on 2013-10-22 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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-Theoretic Aspects of Formal Power Series

Author : Arto Salomaa
Publisher : Springer Science & Business Media
ISBN 13 : 146126264X
Total Pages : 180 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Automata-Theoretic Aspects of Formal Power Series by : Arto Salomaa

Download or read book Automata-Theoretic Aspects of Formal Power Series written by Arto Salomaa and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a theory of formal power series in noncommuting variables, the main emphasis being on results applicable to automata and formal language theory. This theory was initiated around 196O-apart from some scattered work done earlier in connection with free groups-by M. P. Schutzenberger to whom also belong some of the main results. So far there is no book in existence concerning this theory. This lack has had the unfortunate effect that formal power series have not been known and used by theoretical computer scientists to the extent they in our estimation should have been. As with most mathematical formalisms, the formalism of power series is capable of unifying and generalizing known results. However, it is also capable of establishing specific results which are difficult if not impossible to establish by other means. This is a point we hope to be able to make in this book. That formal power series constitute a powerful tool in automata and language theory depends on the fact that they in a sense lead to the arithmetization of automata and language theory. We invite the reader to prove, for instance, Theorem IV. 5. 3 or Corollaries III. 7. 8 and III. 7.- all specific results in language theory-by some other means. Although this book is mostly self-contained, the reader is assumed to have some background in algebra and analysis, as well as in automata and formal language theory.

Cellular Automata and Groups

Author : Tullio Ceccherini-Silberstein
Publisher : Springer Science & Business Media
ISBN 13 : 3642140343
Total Pages : 446 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Cellular Automata and Groups by : Tullio Ceccherini-Silberstein

Download or read book Cellular Automata and Groups written by Tullio Ceccherini-Silberstein and published by Springer Science & Business Media. This book was released on 2010-08-24 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cellular automata were introduced in the first half of the last century by John von Neumann who used them as theoretical models for self-reproducing machines. The authors present a self-contained exposition of the theory of cellular automata on groups and explore its deep connections with recent developments in geometric group theory, symbolic dynamics, and other branches of mathematics and theoretical computer science. The topics treated include in particular the Garden of Eden theorem for amenable groups, and the Gromov-Weiss surjunctivity theorem as well as the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. The volume is entirely self-contained, with 10 appendices and more than 300 exercises, and appeals to a large audience including specialists as well as newcomers in the field. It provides a comprehensive account of recent progress in the theory of cellular automata based on the interplay between amenability, geometric and combinatorial group theory, symbolic dynamics and the algebraic theory of group rings which are treated here for the first time in book form.

Fuzzy Automata and Languages

Author : John N. Mordeson
Publisher : CRC Press
ISBN 13 : 1420035649
Total Pages : 577 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Fuzzy Automata and Languages by : John N. Mordeson

Download or read book Fuzzy Automata and Languages written by John N. Mordeson and published by CRC Press. This book was released on 2002-03-19 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy Automata Theory offers the first in-depth treatment of the theory and mathematics of fuzzy automata and fuzzy languages. It effectively compares and contrasts the different approaches used in fuzzy mathematics and automata and includes complete proofs of the theoretical results presented. More than 60 figures and 125 examples illustrate the results, and exercises in each chapter serve not only to test understanding, but also to present material not covered in detail within the text. Although the book is theoretical in nature, the authors also discuss applications in a variety of fields, including databases, medicine, learning systems, and pattern recognition.