Automata Theory and its Applications

Author: Bakhadyr Khoussainov,Anil Nerode

Publisher: Springer Science & Business Media

ISBN: 1461201713

Category: Mathematics

Page: 432

View: 2460

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.

Formal Languages And Automata Theory

Author: A.A.Puntambekar

Publisher: Technical Publications

ISBN: 9788184313024

Category:

Page: 506

View: 6669

FundamentalsStrings, Alphabet, Language, Operations, Finite state machine, Definitions, Finite automaton model, acceptance of strings and languages, Deterministic finite automaton and non deterministic finite automaton, Transition diagrams and language recognizers.Finite AutomataNFA with Î transitions-Significance, Acceptance of languages. Conversions and Equivalence : Equivalence between NFA with and without Î transitions, NFA to DFA conversion, Minimisation of FSM, Equivalence between two FSM's, Finite Automata with output-Moore and Melay machines.Regular LanguagesRegular sets, Regular expressions, Identify rules, Constructing finite Automata for a given regular expressions, Conversion of finite automata to regular expressions. Pumping lemma of regular sets, Closure properties of regular sets.Grammar FormalismRegular grammars-right linear and left linear grammars, Equivalence between regular linear grammar and FA, Inter conversion, Context free grammar, Derivation trees, Sentential forms,Rightmost and leftmost derivation of strings.Context Free GrammarsAmbiguity in context free grammars. Minimisation of context free grammars. Chomsky normal form, Greiback normal form, Pumping lemma for context free languages. Enumeration of properties of CFL.Push Down AutomataPush down automata, Definition, Model, Acceptance of CFL, Acceptance by final state and acceptance by empty state and its equivalence. Equivalence of CFL and PDA, Interconversion. Introduction to DCFL and DPDA.Turing MachineTuring Machine, Definition, Model, Design of TM, Computable functions, Recursively enumerable languages. Church's hypothesis, Counter machine, Types of turing machines.Computability TheoryChomsky hierarchy of languages, Linear bounded automata and context sensitive language, LR(0) grammar, Decidability of problems, Universal turing machine, Undecidability of posts. Correspondence problem, Turing reducibility, Definition of P and NP problems, NP complete and NP hard problems.

Algebraic and Structural Automata Theory

Author: B. Mikolajczak

Publisher: Elsevier

ISBN: 9780080867847

Category: Mathematics

Page: 401

View: 2993

Automata Theory is part of computability theory which covers problems in computer systems, software, activity of nervous systems (neural networks), and processes of live organisms development. The result of over ten years of research, this book presents work in the following areas of Automata Theory: automata morphisms, time-varying automata, automata realizations and relationships between automata and semigroups. Aimed at those working in discrete mathematics and computer science, parts of the book are suitable for use in graduate courses in computer science, electronics, telecommunications, and control engineering. It is assumed that the reader is familiar with the basic concepts of algebra and graph theory.

Introduction to Automata Theory, Formal Languages and Computation

Author: Shyamalendu Kandar

Publisher: Pearson Education India

ISBN: 9332516324

Category:

Page: 650

View: 6150

Formal languages and automata theory is the study of abstract machines and how these can be used for solving problems. The book has a simple and exhaustive approach to topics like automata theory, formal languages and theory of computation. These descriptions are followed by numerous relevant examples related to the topic. A brief introductory chapter on compilers explaining its relation to theory of computation is also given.

Automata Theory

Author: Matthew Simon

Publisher: World Scientific

ISBN: 9789810237530

Category: Computers

Page: 428

View: 692

This book covers substantially the central ideas of a one semester course in automata theory. It is oriented towards a mathematical perspective that is understandable to non-mathematicians. Comprehension is greatly aided by many examples, especially on the Chomsky ? Schtzenberger theorem, which is not found in most books in this field. Special attention is given to semiautomata theory: the relationship between semigroups and sequential machines (including Green's relations), Schtzenberger's maximal subgroup, von Neumann inverses, wreath products, transducers using matrix notation, shuffle and Kronecker shuffle products. Methods of formal power series, the ambiguity index and linear languages are discussed. Core material includes finite state automata, regular expressions, Kleene's theorem, Chomsky's hierarchy and transformations of grammars. Ambiguous grammars (not limited to context-free grammars) and modal logics are briefly discussed. Turing machine variants with many examples, pushdown automata and their state transition diagrams and parsers, linear-bounded automata/2-PDA and Kuroda normal form are also discussed. A brief study of Lindenmeyer systems is offered as a comparison to the theory of Chomsky.

Applications of Automata Theory and Algebra

Via the Mathematical Theory of Complexity to Biology, Physics, Psychology, Philosophy, and Games

Author: John L. Rhodes,Chrystopher L. Nehaniv

Publisher: World Scientific

ISBN: 9812836969

Category: Mathematics

Page: 274

View: 6404

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.

Automata Theory with Modern Applications

Author: James A. Anderson

Publisher: Cambridge University Press

ISBN: 1139458213

Category: Mathematics

Page: N.A

View: 6067

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.

Formal Languages and Automata Theory

Author: H.S. Behera, Janmenjoy Nayak & Hadibandhu Pattnayak

Publisher: Vikas Publishing House

ISBN: 9325978598

Category: Computers

Page: N.A

View: 1681

The book introduces the fundamental concepts of the theory of computation, formal languages and automata right from the basic building blocks to the depths of the subject. The book begins by giving prerequisites for the subject, like sets, relations and graphs, and all fundamental proof techniques.It proceeds forward to discuss advanced concepts like Turing machine, its language and construction, an illustrated view of the decidability and undecidability of languages along with the post-correspondence problem. KEY FEATURES • Simple and easy-to-follow text • Complete coverage of the subject as per the syllabi of most universities • Discusses advanced concepts like Complexity Theory and various NP-complete problems • More than 250 solved examples

A Half-century of Automata Theory

Celebration and Inspiration

Author: Arto Salomaa,Derick Wood,Sheng Yu

Publisher: World Scientific

ISBN: 9810245904

Category: Computers

Page: 155

View: 5977

This volume gathers lectures by 8 distinguished pioneers of automata theory, including two Turing Award winners. In each contribution, the early developments of automata theory are reminisced about and future directions are suggested. Although some of the contributions go into rather intriguing technical details, most of the book is accessible to a wide audience interested in the progress of the age of computers.The book is a must for professionals in theoretical computer science and related areas of mathematics. For students in these areas it provides an exceptionally deep view at the beginning of the new millennium.

Lectures on automata theory

Author: Juris Hartmanis,S. Ramani

Publisher: N.A

ISBN: N.A

Category: Technology & Engineering

Page: 232

View: 8759

Language and Automata Theory and Applications

4th International Conference, LATA 2010, Trier, Germany, May 24-28, 2010, Proceedings

Author: Carlos Martin-Vide,Henning Fernau,Adrian Horia Dediu

Publisher: Springer

ISBN: 3642130895

Category: Computers

Page: 622

View: 4723

Applied Automata Theory

Author: Julius T. Tou

Publisher: Academic Press

ISBN: 1483225194

Category: Technology & Engineering

Page: 342

View: 6500

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.