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Author : John Carroll,Darrell Long
Publisher : Unknown
Page : 456 pages
File Size : 46,8 Mb
Release : 1989
Category : Computers
ISBN : UOM:39015013480861
Author : Bakhadyr Khoussainov,Anil Nerode
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201717
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 : J. Richard Büchi
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 48,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781461388531
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 : Howard Straubing
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461202899
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 : Mark V. Lawson
Publisher : CRC Press
Page : 324 pages
File Size : 41,8 Mb
Release : 2003-09-17
Category : Mathematics
ISBN : 1584882557
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 : John E. Hopcroft,Rajeev Motwani,Jeffrey D. Ullman
Publisher : Unknown
Page : 488 pages
File Size : 48,5 Mb
Release : 2014
Category : Computational complexity
ISBN : 1292039051
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 : Renji Tao
Publisher : Springer Science & Business Media
Page : 411 pages
File Size : 48,6 Mb
Release : 2009-03-08
Category : Computers
ISBN : 9783540782575
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 : Arto Salomaa
Publisher : Elsevier
Page : 276 pages
File Size : 42,7 Mb
Release : 2014-07-10
Category : Reference
ISBN : 9781483154398
Theory of Automata deals with mathematical aspects of the theory of automata theory, with emphasis on the finite deterministic automaton as the basic model. All other models, such as finite non-deterministic and probabilistic automata as well as pushdown and linear bounded automata, are treated as generalizations of this basic model. The formalism chosen to describe finite deterministic automata is that of regular expressions. A detailed exposition regarding this formalism is presented by considering the algebra of regular expressions. This volume is comprised of four chapters and begins with a discussion on finite deterministic automata, paying particular attention to regular and finite languages; analysis and synthesis theorems; equivalence relations induced by languages; sequential machines; sequential functions and relations; definite languages and non-initial automata; and two-way automata. The next chapter describes finite non-deterministic and probabilistic automata and covers theorems concerning stochastic languages; non-regular stochastic languages; and probabilistic sequential machines. The book then introduces the reader to the algebra of regular expressions before concluding with a chapter on formal languages and generalized automata. Theoretical exercises are included, along with ""problems"" at the end of some sections. This monograph will be a useful resource for beginning graduate or advanced undergraduates of mathematics.
Author : S.P.Eugene Xavier
Publisher : New Age International
Page : 35 pages
File Size : 44,5 Mb
Release : 2005
Category : Computational complexity
ISBN : 9788122416558
This Book Is Aimed At Providing An Introduction To The Basic Models Of Computability To The Undergraduate Students. This Book Is Devoted To Finite Automata And Their Properties. Pushdown Automata Provides A Class Of Models And Enables The Analysis Of Context-Free Languages. Turing Machines Have Been Introduced And The Book Discusses Computability And Decidability. A Number Of Problems With Solutions Have Been Provided For Each Chapter. A Lot Of Exercises Have Been Given With Hints/Answers To Most Of These Tutorial Problems.
Author : Jacques Sakarovitch
Publisher : Cambridge University Press
Page : 922 pages
File Size : 42,6 Mb
Release : 2009-10-01
Category : Mathematics
ISBN : 9781139643795
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.
Author : Daniel I. A. Cohen
Publisher : John Wiley & Sons
Page : 661 pages
File Size : 47,5 Mb
Release : 1996-10-25
Category : Computers
ISBN : 9780471137726
This text strikes a good balance between rigor and an intuitive approach to computer theory. Covers all the topics needed by computer scientists with a sometimes humorous approach that reviewers found "refreshing". It is easy to read and the coverage of mathematics is fairly simple so readers do not have to worry about proving theorems.
Author : Deepak D'Souza
Publisher : World Scientific
Page : 128 pages
File Size : 48,7 Mb
Release : 2012
Category : Electronic
ISBN : 9789814468329
Author : Zvi Kohavi,Niraj K. Jha
Publisher : Cambridge University Press
Page : 128 pages
File Size : 51,7 Mb
Release : 2009-10-22
Category : Computers
ISBN : 9781139483087
Understand the structure, behaviour, and limitations of logic machines with this thoroughly updated third edition. Many new topics are included, such as CMOS gates, logic synthesis, logic design for emerging nanotechnologies, digital system testing, and asynchronous circuit design, to bring students up-to-speed with modern developments. The intuitive examples and minimal formalism of the previous edition are retained, giving students a text that is logical and easy to follow, yet rigorous. Kohavi and Jha begin with the basics, and then cover combinational logic design and testing, before moving on to more advanced topics in finite-state machine design and testing. Theory is made easier to understand with 200 illustrative examples, and students can test their understanding with over 350 end-of-chapter review questions.
Author : Peter Linz
Publisher : Jones & Bartlett Publishers
Page : 408 pages
File Size : 48,6 Mb
Release : 1997
Category : Formal languages
ISBN : UOM:49015002666619
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 : Ding-Zhu Du,Ker-I Ko
Publisher : John Wiley & Sons
Page : 405 pages
File Size : 48,5 Mb
Release : 2004-04-05
Category : Computers
ISBN : 9780471464082
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.