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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: Bakhadyr Khoussainov
Publisher: Springer Science & Business Media
ISBN: 1461201713
Category : Mathematics
Languages : en
Pages : 442
Get Book Here
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: 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: 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: Alexander Meduna
Publisher: Springer Science & Business Media
ISBN: 144710501X
Category : Computers
Languages : en
Pages : 919
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Book Description
A step-by-step development of the theory of automata, languages and computation. Intended for use as the basis of an introductory course at both junior and senior levels, the text is organized so as to allow the design of various courses based on selected material. It features basic models of computation, formal languages and their properties; computability, decidability and complexity; a discussion of modern trends in the theory of automata and formal languages; design of programming languages, including the development of a new programming language; and compiler design, including the construction of a complete compiler. Alexander Meduna uses clear definitions, easy-to-follow proofs and helpful examples to make formerly obscure concepts easy to understand. He also includes challenging exercises and programming projects to enhance the reader's comprehension, and many 'real world' illustrations and applications in practical computer science.
Author: James A. Anderson
Publisher: Cambridge University Press
ISBN: 1139458213
Category : Mathematics
Languages : en
Pages : 3
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Book Description
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.
Author: Kendall Preston Jr.
Publisher: Springer Science & Business Media
ISBN: 1489903933
Category : Computers
Languages : en
Pages : 354
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Book Description
It is with great pleasure that I present this fourth vol ume in the series "Advanced Applications in Pattern Recognition." It would be difficult to find two authors better versed in the design and application of parallel image processing systems, due to both their own many years of pioneering in the field and their encyclopedic knowledge of what is going on in uni versity and industrial laboratories around the world. The monograph is unique in its parallel presentation of orthogonal and hexagonal dissections, and the wealth of graphic illustration of algorithmic procedures for processing and analyz ing images in the various known implementations of parallel im age-processing architectures. This volume should find a place on the bookshelf of every practitioner of pattern recognition, image processing, and compu ter graphics. Morton Nadler General Editor vii PREFACE This book endeavors to introduce the reader to the subject of cellular logic and cellular automata and is devoted particu larly to those parts dealing with the manipulation of pictorial data. The study of cellular automata owes much to the pioneer ing work of John von Neumann during the 1950s. Von Neumann was interested in general problems in the behavior of computing structures and was immensely impressed by the complexity and performance of the human brain, which he felt must point to wards successful designs for automatic computing machines.
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: Parimal Pal Chaudhuri
Publisher: John Wiley & Sons
ISBN: 9780818677175
Category : Technology & Engineering
Languages : en
Pages : 372
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Book Description
This book presents an extensive survey and report of related research on important developments in cellular automata (CA) theory. The authors introduce you to this theory in a comprehensive manner that will help you understand the basics of CA and be prepared for further research. They illustrate the matrix algebraic tools that characterize group CA and help develop its applications in the field of VLSI testing. The text examines schemes based on easily testable FSM, bit-error correcting code, byte error correcting code, and characterization of 2D cellular automata. In addition, it looks into CA-based universal pattern generation, data encryption, and synthesis of easily testable combinational logic. The book covers new characterizations of group CA behavior, CA-based tools for fault diagnosis, and a wide variety of applications to solve real-life problems.
Author: Carlos Martín-Vide
Publisher: Springer
ISBN: 3030134350
Category : Computers
Languages : en
Pages : 474
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Book Description
This book constitutes the refereed proceedings of the 13th International Conference on Language and Automata Theory and Applications, LATA 2019, held in St. Petersburg, Russia, in March 2019. The 31 revised full papers presented together with 5 invited talks were carefully reviewed and selected from 98 submissions. The papers cover the following topics: Automata; Complexity; Grammars; Languages; Graphs, trees and rewriting; and Words and codes.
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.
