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Author: Howard Straubing
Publisher: Springer Science & Business Media
ISBN: 1461202892
Category : Computers
Languages : en
Pages : 235
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Book Description
The study of the connections between mathematical automata and for mal logic is as old as theoretical computer science itself. In the founding paper of the subject, published in 1936, Turing showed how to describe the behavior of a universal computing machine with a formula of first order predicate logic, and thereby concluded that there is no algorithm for deciding the validity of sentences in this logic. Research on the log ical aspects of the theory of finite-state automata, which is the subject of this book, began in the early 1960's with the work of J. Richard Biichi on monadic second-order logic. Biichi's investigations were extended in several directions. One of these, explored by McNaughton and Papert in their 1971 monograph Counter-free Automata, was the characterization of automata that admit first-order behavioral descriptions, in terms of the semigroup theoretic approach to automata that had recently been developed in the work of Krohn and Rhodes and of Schiitzenberger. In the more than twenty years that have passed since the appearance of McNaughton and Papert's book, the underlying semigroup theory has grown enor mously, permitting a considerable extension of their results. During the same period, however, fundamental investigations in the theory of finite automata by and large fell out of fashion in the theoretical com puter science community, which moved to other concerns.
Author: Howard Straubing
Publisher: Springer Science & Business Media
ISBN: 1461202892
Category : Computers
Languages : en
Pages : 235
Get Book Here
Book Description
The study of the connections between mathematical automata and for mal logic is as old as theoretical computer science itself. In the founding paper of the subject, published in 1936, Turing showed how to describe the behavior of a universal computing machine with a formula of first order predicate logic, and thereby concluded that there is no algorithm for deciding the validity of sentences in this logic. Research on the log ical aspects of the theory of finite-state automata, which is the subject of this book, began in the early 1960's with the work of J. Richard Biichi on monadic second-order logic. Biichi's investigations were extended in several directions. One of these, explored by McNaughton and Papert in their 1971 monograph Counter-free Automata, was the characterization of automata that admit first-order behavioral descriptions, in terms of the semigroup theoretic approach to automata that had recently been developed in the work of Krohn and Rhodes and of Schiitzenberger. In the more than twenty years that have passed since the appearance of McNaughton and Papert's book, the underlying semigroup theory has grown enor mously, permitting a considerable extension of their results. During the same period, however, fundamental investigations in the theory of finite automata by and large fell out of fashion in the theoretical com puter science community, which moved to other concerns.
Author: John Carroll
Publisher:
ISBN:
Category : Computers
Languages : en
Pages : 456
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Book Description
Author: J. Richard Büchi
Publisher: Springer Science & Business Media
ISBN: 1461388538
Category : Mathematics
Languages : en
Pages : 335
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Book Description
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.
Author: John E. Hopcroft
Publisher:
ISBN: 9781292039053
Category : Computational complexity
Languages : en
Pages : 488
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Book Description
This classic book on formal languages, automata theory, and computational complexity has been updated to present theoretical concepts in a concise and straightforward manner with the increase of hands-on, practical applications. This new edition comes with Gradiance, an online assessment tool developed for computer science. Please note, Gradiance is no longer available with this book, as we no longer support this product.
Author: Mark V. Lawson
Publisher: CRC Press
ISBN: 9781584882558
Category : Mathematics
Languages : en
Pages : 324
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Book Description
Interest in finite automata theory continues to grow, not only because of its applications in computer science, but also because of more recent applications in mathematics, particularly group theory and symbolic dynamics. The subject itself lies on the boundaries of mathematics and computer science, and with a balanced approach that does justice to both aspects, this book provides a well-motivated introduction to the mathematical theory of finite automata. The first half of Finite Automata focuses on the computer science side of the theory and culminates in Kleene's Theorem, which the author proves in a variety of ways to suit both computer scientists and mathematicians. In the second half, the focus shifts to the mathematical side of the theory and constructing an algebraic approach to languages. Here the author proves two main results: Schützenberger's Theorem on star-free languages and the variety theorem of Eilenberg and Schützenberger. Accessible even to students with only a basic knowledge of discrete mathematics, this treatment develops the underlying algebra gently but rigorously, and nearly 200 exercises reinforce the concepts. Whether your students' interests lie in computer science or mathematics, the well organized and flexible presentation of Finite Automata provides a route to understanding that you can tailor to their particular tastes and abilities.
Author: Ding-Zhu Du
Publisher: John Wiley & Sons
ISBN: 0471464082
Category : Computers
Languages : en
Pages : 405
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Book Description
Automata and natural language theory are topics lying at the heart of computer science. Both are linked to computational complexity and together, these disciplines help define the parameters of what constitutes a computer, the structure of programs, which problems are solvable by computers, and a range of other crucial aspects of the practice of computer science. In this important volume, two respected authors/editors in the field offer accessible, practice-oriented coverage of these issues with an emphasis on refining core problem solving skills.
Author: Renji Tao
Publisher: Springer Science & Business Media
ISBN: 3540782575
Category : Computers
Languages : en
Pages : 411
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Book Description
Finite Automata and Application to Cryptography mainly deals with the invertibility theory of finite automata and its application to cryptography. In addition, autonomous finite automata and Latin arrays, which are relative to the canonical form for one-key cryptosystems based on finite automata, are also discussed. Finite automata are regarded as a natural model for ciphers. The Ra Rb transformation method is introduced to deal with the structure problem of such automata; then public key cryptosystems based on finite automata and a canonical form for one-key ciphers implementable by finite automata with bounded-error-propagation and without data expansion are proposed. The book may be used as a reference for computer science and mathematics majors, including seniors and graduate students. Renji Tao is a Professor at the Institute of Software, Chinese Academy of Sciences, Beijing.
Author: Peter Linz
Publisher: Jones & Bartlett Publishers
ISBN:
Category : Computers
Languages : en
Pages : 408
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Book Description
An Introduction to Formal Languages & Automata provides an excellent presentation of the material that is essential to an introductory theory of computation course. The text was designed to familiarize students with the foundations & principles of computer science & to strengthen the students' ability to carry out formal & rigorous mathematical argument. Employing a problem-solving approach, the text provides students insight into the course material by stressing intuitive motivation & illustration of ideas through straightforward explanations & solid mathematical proofs. By emphasizing learning through problem solving, students learn the material primarily through problem-type illustrative examples that show the motivation behind the concepts, as well as their connection to the theorems & definitions.
Author: Maxim Mozgovoy
Publisher: Jones & Bartlett Learning
ISBN: 1449633234
Category : Computers
Languages : en
Pages : 359
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Book Description
Algorithms, Languages, Automata, & Compilers A Practical Approach is designed to cover the standard “theory of computing” topics through a strong emphasis on practical applications rather than theorems and proofs. Finite automata, Turing machines, models of computation, complexity, solvability, and other topics that form a foundation of modern programming are discussed -first with a gentle theoretical orientation, and then applied through programming code and practical examples. JFLAP projects and applications are integrated throughout the book, and C# is used for all code.
Author: Stefan Hollos
Publisher: Abrazol Publishing
ISBN: 9781887187169
Category : Computers
Languages : en
Pages : 154
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Book Description
This is a book about solving problems related to automata and regular expressions. It helps you learn the subject in the most effective way possible, through problem solving. There are 84 problems with solutions. The introduction provides some background information on automata, regular expressions, and generating functions. The inclusion of generating functions is one of the unique features of this book. Few computer science books cover the topic of generating functions for automata and there are only a handful of combinatorics books that mention it. This is unfortunate since we believe the connection between computer science and combinatorics, that is opened up by these generating functions, can enrich both subjects and lead to new methods and applications. We cover a few interesting classes of problems for finite state automata and then show some examples of infinite state automata and recursive regular expressions. The final problem in the book involves constructing a recursive regular expression for matching regular expressions. This book explains: * Why automata are important. * The relationship of automata to regular expressions. * The difference between deterministic and nondeterministic automata. * How to get the regular expression from an automaton. * Why two seemingly different regular expressions can belong to the same automaton. * How the regular expression for an infinite automaton is different than one for a finite one. * The relationship of a regular expression to a regular language. * What a generating function for a language tells you about the language. * How to get a generating function from a regular expression. * How the generating function of a recursive regular expression is different from that of an ordinary regular expression. * How to test divisibility properties of integers (binary and decimal based) using automata. * How to construct an automaton to search for a given pattern, or for a given pattern not occurring. * How to construct an automaton for arbitrary patterns and alphabets. * How the recursive regular expression for nested parentheses leads to the Catalan numbers. Included in this book: * Divisibility problems in binary and decimal. * Pattern search problems in binary, ternary, and quaternary alphabets. * Pattern search problems for circular strings that contain or do not contain a given pattern. * Automata, regular expressions, and generating functions for gambling games. * Automata and generating functions for finite and infinite correctly nested parentheses. * The recursive regular expression for matching regular expressions over a binary alphabet. * A further reading list.
