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Author: John L. Rhodes
Publisher: World Scientific
ISBN: 9812836969
Category : Mathematics
Languages : en
Pages : 293
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Book Description
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 The unpublished manuscript, often referred to as "The Wild Book," became an underground classic, continually requested in manuscript form, and read by many leading researchers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.
Author: John L. Rhodes
Publisher: World Scientific
ISBN: 9812836969
Category : Mathematics
Languages : en
Pages : 293
Get Book Here
Book Description
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.
Author: Jirí Adámek
Publisher: Springer Science & Business Media
ISBN: 9780792300106
Category : Mathematics
Languages : en
Pages : 498
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Book Description
Monograph( based very largely upon results original to the Czechoslovakian authors) presents an abstract account of the theory of automata for sophisticated readers presumed to be already conversant in the language of category theory. The seven chapters are punctuated at frequent intervals by exampl
Author: Bakhadyr Khoussainov
Publisher: Springer Science & Business Media
ISBN: 1461201713
Category : Mathematics
Languages : en
Pages : 442
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Book Description
The theory of finite automata on finite stings, infinite strings, and trees has had a dis tinguished history. First, automata were introduced to represent idealized switching circuits augmented by unit delays. This was the period of Shannon, McCullouch and Pitts, and Howard Aiken, ending about 1950. Then in the 1950s there was the work of Kleene on representable events, of Myhill and Nerode on finite coset congruence relations on strings, of Rabin and Scott on power set automata. In the 1960s, there was the work of Btichi on automata on infinite strings and the second order theory of one successor, then Rabin's 1968 result on automata on infinite trees and the second order theory of two successors. The latter was a mystery until the introduction of forgetful determinacy games by Gurevich and Harrington in 1982. Each of these developments has successful and prospective applications in computer science. They should all be part of every computer scientist's toolbox. Suppose that we take a computer scientist's point of view. One can think of finite automata as the mathematical representation of programs that run us ing fixed finite resources. Then Btichi's SIS can be thought of as a theory of programs which run forever (like operating systems or banking systems) and are deterministic. Finally, Rabin's S2S is a theory of programs which run forever and are nondeterministic. Indeed many questions of verification can be decided in the decidable theories of these automata.
Author: Elaine Rich
Publisher: Prentice Hall
ISBN: 0132288060
Category : Computers
Languages : en
Pages : 1120
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Book Description
For upper level courses on Automata. Combining classic theory with unique applications, this crisp narrative is supported by abundant examples and clarifies key concepts by introducing important uses of techniques in real systems. Broad-ranging coverage allows instructors to easily customise course material to fit their unique requirements.
Author: Jean Berstel
Publisher: Cambridge University Press
ISBN: 052188831X
Category : Computers
Languages : en
Pages : 634
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Book Description
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.
Author: Jean Berstel
Publisher: Cambridge University Press
ISBN: 0521190223
Category : Mathematics
Languages : en
Pages : 263
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Book Description
A modern account of the subject and its applications. Excellent resource for those working in algebra and theoretical computer science.
Author: John N. Mordeson
Publisher: CRC Press
ISBN: 1420035649
Category : Computers
Languages : en
Pages : 577
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Book Description
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.
Author: Paul M. Cohn
Publisher: Springer Science & Business Media
ISBN: 1447100395
Category : Mathematics
Languages : en
Pages : 454
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Book Description
Here is the second volume of a revised edition of P.M. Cohn's classic three-volume text Algebra, widely regarded as one of the most outstanding introductory algebra textbooks. Volume Two focuses on applications. The text is supported by worked examples, with full proofs, there are numerous exercises with occasional hints, and some historical remarks.
Author: M. Holcombe
Publisher: Cambridge University Press
ISBN: 9780521604925
Category : Computers
Languages : en
Pages : 248
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Book Description
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...
Author: Klaus Denecke
Publisher: CRC Press
ISBN: 1482285835
Category : Mathematics
Languages : en
Pages : 396
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Book Description
Over the past 20 years, the emergence of clone theory, hyperequational theory, commutator theory and tame congruence theory has led to a growth of universal algebra both in richness and in applications, especially in computer science. Yet most of the classic books on the subject are long out of print and, to date, no other book has integrated these theories with the long-established work that supports them. Universal Algebra and Applications in Theoretical Computer Science introduces the basic concepts of universal algebra and surveys some of the newer developments in the field. The first half of the book provides a solid grounding in the core material. A leisurely pace, careful exposition, numerous examples, and exercises combine to form an introduction to the subject ideal for beginning graduate students or researchers from other areas. The second half of the book focuses on applications in theoretical computer science and advanced topics, including Mal'cev conditions, tame congruence theory, clones, and commutators. The impact of the advances in universal algebra on computer science is just beginning to be realized, and the field will undoubtedly continue to grow and mature. Universal Algebra and Applications in Theoretical Computer Science forms an outstanding text and offers a unique opportunity to build the foundation needed for further developments in its theory and in its computer science applications.
