Introducing the Theory of Computation is the ideal text for any undergraduate, introductory course on formal languages, automata, and computability. The author provides a concise, yet complete, introduction to the important models of finite automata, grammars, and Turing machines, as well as to undecidability and the basics of complexity theory. Numerous problems, varying in level of difficulty, round out each chapter and allow students to test themselves on key topics. Answers to selected exercises are included as an appendix and a complete instructor's solutions manual is available on the text's website.
Introducing the Theory of Computation is the ideal text for any undergraduate, introductory course on formal languages, automata, and computability.
Author: Wayne Goddard
Publisher: Jones & Bartlett Learning
Introducing the Theory of Computation is the ideal text for any undergraduate, introductory course on formal languages, automata, and computability. The author provides a concise, yet complete introduction to the important models of finite automata, grammars, and Turing machines, as well as undecidability and the basics of complexity theory. Numerous problems and programming exercises, varying in level of difficulty, round out each chapter and allow students to test themselves on key topics. Answers to selected exercises are included as an appendix and a complete instructor s solutions manual is available on the text s web site.
Introducing the Theory of Computation is the ideal text for any undergraduate, introductory course on formal languages, automata, and computability.
Discusses such topics as: regular languages; context-free languages; Church-Turing thesis; decidability; reducibility; the recursion theorem; time complexity; space complexity; and provable intractability.
I have tried to make both the Exercises and Problems interesting challenges . PRELIMINARY EDITION This edition of Introduction to the Theory of Computation ...
Author: Michael Sipser
Category: Computational complexity
The foundation of computer science is built upon the following questions: What is an algorithm? What can be computed and what cannot be computed? What does it mean for a function to be computable? How does computational power depend upon programming constructs? Which algorithms can be considered feasible? For more than 70 years, computer scientists are searching for answers to such qu- tions. Their ingenious techniques used in answering these questions form the theory of computation. Theory of computation deals with the most fundamental ideas of computer s- ence in an abstract but easily understood form. The notions and techniques employed are widely spread across various topics and are found in almost every branch of c- puter science. It has thus become more than a necessity to revisit the foundation, learn the techniques, and apply them with con?dence. Overview and Goals This book is about this solid, beautiful, and pervasive foundation of computer s- ence. It introduces the fundamental notions, models, techniques, and results that form the basic paradigms of computing. It gives an introduction to the concepts and mathematics that computer scientists of our day use to model, to argue about, and to predict the behavior of algorithms and computation. The topics chosen here have shown remarkable persistence over the years and are very much in current use.
It has thus become more than a necessity to revisit the foundation, learn the techniques, and apply them with con?dence. Overview and Goals This book is about this solid, beautiful, and pervasive foundation of computer s- ence.
Author: Arindama Singh
Publisher: Springer Science & Business Media
The aim of this textbook is to present an account of the theory of computation. After introducing the concept of a model of computation and presenting various examples, the author explores the limitations of effective computation via basic recursion theory. Self-reference and other methods are introduced as fundamental and basic tools for constructing and manipulating algorithms. From there the book considers the complexity of computations and the notion of a complexity measure is introduced. Finally, the book culminates in considering time and space measures and in classifying computable functions as being either feasible or not. The author assumes only a basic familiarity with discrete mathematics and computing, making this textbook ideal for a graduate-level introductory course. It is based on many such courses presented by the author and so numerous exercises are included. In addition, the solutions to most of these exercises are provided.
Self-reference and other methods are introduced as fundamental and basic tools for constructing and manipulating algorithms. From there the book considers the complexity of computations and the notion of a complexity measure is introduced.
Author: Carl Smith
Quantum computation, one of the latest joint ventures between physics and the theory of computation, is a scientific field whose main goals include the development of hardware and algorithms based on the quantum mechanical properties of those physical systems used to implement such algorithms. Solving difficult tasks (for example, the Satisfiability Problem and other NP-complete problems) requires the development of sophisticated algorithms, many ofwhich employ stochastic processes as their mathematical basis. Discrete random walks are a popular choice among those stochastic processes. Inspired on the success of discrete random walks in algorithm development, quantum walks, an emerging field of quantum computation, is a generalization of random walks into the quantum mechanical world. The purpose of this lecture is to provide a concise yet comprehensive introduction to quantum walks. Table of Contents: Introduction / Quantum Mechanics / Theory of Computation / Classical Random Walks / Quantum Walks / Computer Science and Quantum Walks / Conclusions
The purpose of this chapter is to concisely introduce the Theory of Computation, in order to provide the necessary background and to motivate our further discussion on the importance of classical random walks and quantum walks in ...
Author: Salvador Venegas-Andraca
Publisher: Morgan & Claypool Publishers
An accessible and rigorous textbook for introducing undergraduates to computer science theory What Can Be Computed? is a uniquely accessible yet rigorous introduction to the most profound ideas at the heart of computer science. Crafted specifically for undergraduates who are studying the subject for the first time, and requiring minimal prerequisites, the book focuses on the essential fundamentals of computer science theory and features a practical approach that uses real computer programs (Python and Java) and encourages active experimentation. It is also ideal for self-study and reference. The book covers the standard topics in the theory of computation, including Turing machines and finite automata, universal computation, nondeterminism, Turing and Karp reductions, undecidability, time-complexity classes such as P and NP, and NP-completeness, including the Cook-Levin Theorem. But the book also provides a broader view of computer science and its historical development, with discussions of Turing's original 1936 computing machines, the connections between undecidability and Gödel's incompleteness theorem, and Karp's famous set of twenty-one NP-complete problems. Throughout, the book recasts traditional computer science concepts by considering how computer programs are used to solve real problems. Standard theorems are stated and proven with full mathematical rigor, but motivation and understanding are enhanced by considering concrete implementations. The book's examples and other content allow readers to view demonstrations of—and to experiment with—a wide selection of the topics it covers. The result is an ideal text for an introduction to the theory of computation. An accessible and rigorous introduction to the essential fundamentals of computer science theory, written specifically for undergraduates taking introduction to the theory of computation Features a practical, interactive approach using real computer programs (Python in the text, with forthcoming Java alternatives online) to enhance motivation and understanding Gives equal emphasis to computability and complexity Includes special topics that demonstrate the profound nature of key ideas in the theory of computation Lecture slides and Python programs are available at whatcanbecomputed.com
The book covers the standard topics in the theory of computation, including Turing machines and finite automata, universal computation, nondeterminism, Turing and Karp reductions, undecidability, time-complexity classes such as P and NP, ...
Author: John MacCormick
Publisher: Princeton University Press
Theory and Computation of Tensors: Multi-Dimensional Arrays investigates theories and computations of tensors to broaden perspectives on matrices. Data in the Big Data Era is not only growing larger but also becoming much more complicated. Tensors (multi-dimensional arrays) arise naturally from many engineering or scientific disciplines because they can represent multi-relational data or nonlinear relationships. Provides an introduction of recent results about tensors Investigates theories and computations of tensors to broaden perspectives on matrices Discusses how to extend numerical linear algebra to numerical multi-linear algebra Offers examples of how researchers and students can engage in research and the applications of tensors and multi-dimensional arrays
This book is devoted to the theory and computation of tensors, also called hypermatrices. ... We first propose a fast algorithm for Hankel tensor-vector products by introducing a special class of Hankel tensors that can be diagonalized ...
Author: Yimin Wei
Publisher: Academic Press
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.
Introducing more '1', S is replaced by another non-terminal A. The grammar for the language is S → 0S1/A1/1 A→A1/ε ... From the previous discussion, the grammar is S → A.B 32 IntroductiontoAutomataTheory,FormalLanguagesandComputation.
Author: Shyamalendu Kandar
Publisher: Pearson Education India
Comprehensive introduction to the neural network models currently under intensive study for computational applications. It also provides coverage of neural network applications in a variety of problems of both theoretical and practical interest.
With this most of the computer science community left the neural network paradigm for almost 20 years. Still, there were a number of people who continued to develop neural network theory in the 1970's.
Author: John A. Hertz
Publisher: CRC Press
The study of hydrodynamic stability is fundamental to many subjects, ranging from geophysics and meteorology through to engineering design. This treatise covers both classical and modern aspects of the subject, systematically developing it from the simplest physical problems, then progressing to the most complex, considering linear and nonlinear situations, and analyzing temporal and spatial stability. The authors examine each problem both analytically and numerically. Many relevant fluid flows are treated, including those where the fluid may be compressible, or those from geophysics, or those that require salient geometries for description. Details of initial-value problems are explored equally with those of stability. The text includes copious illustrations and an extensive bibliography, making it suitable for courses on hydrodynamic stability or as an authoritative reference for researchers. In this second edition the opportunity has been taken to update the text and, most importantly, provide solutions to the numerous extended exercises.
13.3.1 Natural Disturbances Although introducing artificial disturbances can be extremely beneficial to study numerous physical phenomena associated with the transition process, understanding the natural ingestion of disturbances has in ...
Author: W. O. Criminale
Publisher: Cambridge University Press
The study of hydrodynamic stability is fundamental to many subjects, ranging from geophysics and meteorology through to engineering design. This treatise covers both classical and modern aspects of the subject, systematically developing it from the simplest physical problems, then progressing chapter by chapter to the most complex, considering linear and nonlinear situations, and analysing temporal and spatial stability. The authors examine each problem both analytically and numerically: many chapters end with an appendix outlining relevant numerical techniques. All relevant fluid flows are treated, including those where the fluid may be compressible, or those from geophysics, or those that require salient geometries for description. Details of initial-value problems are explored equally with those of stability. As a result, the early transient period as well as the asymptotic fate for perturbations for a flow can be assessed. The text is enriched with many exercises, copious illustrations and an extensive bibliography and the result is a book that can be used with courses on hydrodynamic stability or as an authoritative reference for researchers.
13.3.1 Natural disturbances Although introducing artificial disturbances can be extremely beneficial to study numerous physical phenomena associated with the transition process, understanding the natural ingestion of disturbances has in ...
Author: W. O. Criminale
Publisher: Cambridge University Press
Problem solving in computing is referred to as computational thinking. The theory behind this concept is challenging in its technicalities, yet simple in its ideas. This book introduces the theory of computation from its inception to current form of complexity; from explanations of how the field of computer science was formed using classical ideas in mathematics by Gödel, to conceptualization of the Turing Machine, to its more recent innovations in quantum computation, hypercomputation, vague computing and natural computing. It describes the impact of these in relation to academia, business and wider society, providing a sound theoretical basis for its practical application. Written for accessibility, Demystifying Computation provides the basic knowledge needed for non-experts in the field, undergraduate computer scientists and students of information and communication technology and software development. Request Inspection Copy Contents:A Brief History of ComputingFrom Hilbert to Gödel to TuringHypercomputationNatural ComputingQuantum ComputingVague ComputingPhysical Reality and Computation Readership: High-School and undergraduate students in computer science, information and communication technology, and software development, and non-experts in the field looking to understand how computation works.
In the 1930s, three seemingly different mathematical models of computation were put forth as an attempt to solve this problem. How and why these models emerged as well as their impact on the development of the theory of computation is ...
Author: Apostolos Syropoulos
Publisher: World Scientific Publishing Company
A survey of computational methods for understanding, generating, and manipulating human language, which offers a synthesis of classical representations and algorithms with contemporary machine learning techniques. This textbook provides a technical perspective on natural language processing—methods for building computer software that understands, generates, and manipulates human language. It emphasizes contemporary data-driven approaches, focusing on techniques from supervised and unsupervised machine learning. The first section establishes a foundation in machine learning by building a set of tools that will be used throughout the book and applying them to word-based textual analysis. The second section introduces structured representations of language, including sequences, trees, and graphs. The third section explores different approaches to the representation and analysis of linguistic meaning, ranging from formal logic to neural word embeddings. The final section offers chapter-length treatments of three transformative applications of natural language processing: information extraction, machine translation, and text generation. End-of-chapter exercises include both paper-and-pencil analysis and software implementation. The text synthesizes and distills a broad and diverse research literature, linking contemporary machine learning techniques with the field's linguistic and computational foundations. It is suitable for use in advanced undergraduate and graduate-level courses and as a reference for software engineers and data scientists. Readers should have a background in computer programming and college-level mathematics. After mastering the material presented, students will have the technical skill to build and analyze novel natural language processing systems and to understand the latest research in the field.
Ideas from linguistics are introduced throughout the text as needed, including discussions of morphology and syntax (chapter 9), ... (2009); for an introduction to the theory of computation, see Arora and Barak (2009) and Sipser (2012).
Author: Jacob Eisenstein
Publisher: MIT Press
Presents easily accessible coverage of language theory, concentrating on the major properties of the fundamental and automata models for languages. Focuses on practical applications such as finite automata and pattern matching, regular expressions and text editing, extended context-free grammars, and syntax diagrams. Simple and elegant proofs are given for theorems usually considered difficult (e.g., Parikh's theorem or the proof that every finite automata has an equivalent regular expression). Provides algorithms in a Pascal-like notation which complement discussions of constructions and programming. Each chapter includes a springboard section introducing topics for further investigation. Also provides short exercises and programming projects plus extensive examples.
Presents easily accessible coverage of language theory, concentrating on the major properties of the fundamental and automata models for languages.
Author: Derrick Wood
The book is about the key elements required for designing, building and controlling effective artificial swarms comprised of multiple moving physical agents. Therefore this book presents the fundamentals of each of those key elements in the particular frame of dynamic swarming, specifically exposing the profound connections between these elements and establish some general design principles for swarming behaviors. This scientific endeavor requires an inter-disciplinary approach: biomimetic inspiration from ethology and ecology, study of social information flow, analysis of temporal and adaptive signaling network of interaction, considerations of control of networked real-time systems, and lastly, elements of complex adaptive dynamical systems. This book offers a completely new perspective on the scientific understanding of dynamic collective behaviors thanks to its multi-disciplinary approach and its focus on artificial swarm of physical agents. Two of the key problems in understanding the emergence of swarm intelligent behaviors are identifying the social interaction rules a.k.a. the behavioral algorithm and uncovering how information flows between swarming agents. While most books about swarm dynamics have been focusing on the former, this book emphasizes the much-less discussed topic of distributed information flow, always with the aim of establishing general design principles.
The objective of this section is not to give a complete introduction to the theory of computation (interested readers are referred to the classic monograph by Sipser  or other similar general references) but instead to briefly ...
Author: Roland Bouffanais
Category: Technology & Engineering
Modular Forms is a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to various subjects, such as the theory of quadratic forms, the proof of Fermat's Last Theorem and the approximation of π. The text gives a balanced overview of both the theoretical and computational sides of its subject, allowing a variety of courses to be taught from it. This second edition has been revised and updated. New material on the future of modular forms as well as a chapter about longer-form projects for students has also been added.
This book concentrates on the computational aspects of the theory of modular forms, but at the same time also gives a grounding in the classical and theoretical aspects of modular forms. We now list some possible courses which could be ...
Author: L J P Kilford
Publisher: World Scientific Publishing Company
The Concise Encyclopedia of Computer Science has been adapted from the full Fourth Edition to meet the needs of students, teachers and professional computer users in science and industry. As an ideal desktop reference, it contains shorter versions of 60% of the articles found in the Fourth Edition, putting computer knowledge at your fingertips. Organised to work for you, it has several features that make it an invaluable and accessible reference. These include: Cross references to closely related articles to ensure that you don’t miss relevant information Appendices covering abbreviations and acronyms, notation and units, and a timeline of significant milestones in computing have been included to ensure that you get the most from the book. A comprehensive index containing article titles, names of persons cited, references to sub-categories and important words in general usage, guarantees that you can easily find the information you need. Classification of articles around the following nine main themes allows you to follow a self study regime in a particular area: Hardware Computer Systems Information and Data Software Mathematics of Computing Theory of Computation Methodologies Applications Computing Milieux. Presenting a wide ranging perspective on the key concepts and developments that define the discipline, the Concise Encyclopedia of Computer Science is a valuable reference for all computer users.
Neural Nets In 1943 , McCulloch and Pitts introduced nets of formalized neurons and showed that such neural nets could ... In 1948 , von Neumann added to the computational and logical questions of automata theory by introducing new ...
Author: Edwin D. Reilly
Publisher: John Wiley & Sons
What is the physics of life and why does it matter? The essays in this book probe this question, celebrating modern biology's vibrant dialog with theoretical physics — a scientific adventure in which biological understanding is enriched by physical theory without losing its own inherent traditions and perspectives. The book explores organic complexity and self-organization through research applications to embryology, cell biology, behavioral neuroscience, and evolution. The essays will excite the interest of physics students in thinking about biology's “grand challenges”, in part by means of self-contained introductions to theoretical computer science, symmetry methods in bifurcation theory, and evolutionary games. Seasoned investigators in both the physical and life sciences will also find challenging ideas and applications presented in this volume. This is a Print On Demand title. We no longer stock the original but will recreate a copy for you. While all efforts are made to ensure that quality is the same as the original, there may be differences in some areas of the design and packaging. Contents:Foundations:Emergence in Physics and Biology (L E H Trainor)Holism and Reduction (C J Lumsden)Complexity: A Pluralistic Approach (W A M Brandts)Dynamics, Complexity and Computation (P A Dufort & C J Lumsden)Development: Field Approaches to Pattern Formation:Vector Field Models of Morphogenesis (W A M Brandts & J Totafurno)Symmetry Breaking Bifurcations (T M Hart & L E H Trainor)Development: Principles of Self-Organization:Generic Dynamics of Morphogenesis (B Goodwin)Toward a Model of Growth and Form in Living Systems (F Cummings)Living Organization, the Coherence of Organisms and the Morphogenetic Field (M W Ho et al.)Is Spatial Pattern Formation Homologous in Unicellular and Multicellular Organisms? (J Frankel)Cellular and Organismic Biology:Statistical Mechanics of the Main Phase Transition in Lipid Bilayers (F P Jones & P Tevlin)Multi-Neuron Interactions in Neural Network Models of Associative Memory (A E Busch & L E H Trainor)Network Hierarchies in Neural Organization, Development and Pathology (J P Sutton)Category Switching — A Neural Network Approach (L E H Trainor et al.)Evolution:A Model of Molecular Evolution Based on the Statistical Analysis of Nucleotide Sequences (L Luo)Codon Space: Exploring the Origins and Development of the Genetic Code (L E H Trainor et al.)Evolution of Development: The Shuffling of Ancient Modules by Ubiquitous Bureaucracies (E W Larsen)Game Theory in Biology (G W A Rowe) Readership: Physicial scientists, biologists, engineers, applied mathematicians and philosophers. keywords:Holism and Reductionism;Complexity;Symmetry;Emergent Property;Patterns;Neural Interactions;Statistical Models;Game Theory;Biology;Morphogenesis;Morphogens;Pattern Formation;Development;Epithelia Folding;Biological Modeling;Complexity;Physical Theory;Biological Regulation;Pattern Formation;Nonlinear Dynamics;Evolution;Developmental Field;Neural Networks;Collective Behavior;Genetic Code;Emergence;Reductionism;Holism;Self-Organization;Bifurcation Theory;Morphogenetic Field;Regeneration;Phase Transitions in Bilayers;Task Switching;Nucleotide Sequences;Molecular Evolution “The important issue here is not what physics theory has done for biology (which is not very much), but what it can do in the future, and to this end the book does a marvellous job of defining the arena.” Nature “… the scope of the articles is broad … The book should be of interest to scientists coming from biological, physical and mathematical sciences.”Bulletin for Mathematical Biology
We have therefore included material introducing mathematical game theory, computation theory and bifurcation symmetries in a manner that hopefully will make apparent their cutting-edge importance for biology while setting the stage for ...
Author: Charles J Lumsden
Publisher: World Scientific
This volume - honoring the computer science pioneer Joseph Goguen on his 65th Birthday - includes 32 refereed papers by leading researchers in areas spanned by Goguen's work. The papers address a variety of topics from meaning, meta-logic, specification and composition, behavior and formal languages, as well as models, deduction, and computation, by key members of the research community in computer science and other fields connected with Joseph Goguen's work.
“OBJ–O Preliminary User Manual,” with Joseph Tardo, Semantics and Theory of Computation Report Number 10, Computer Science Department, University of California at Los Angeles, July 1977. “Introducing Variables (Extended Abstract),” with ...
Author: Kokichi Futatsugi