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Automata, Computability and Complexity: Theory and Applications

Automata, Computability and Complexity: Theory and Applications

          
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About the Book

The theoretical underpinnings of computing form a standard part of almost every computer science curriculum. But the classic treatment of this material isolates it from the myriad ways in which the theory influences the design of modern hardware and software systems. The goal of this book is to change that. The book is organized into a core set of chapters (that cover the standard material suggested by the title), followed by a set of appendix chapters that highlight application areas including programming language design, compilers, software verification, networks, security, natural language processing, artificial intelligence, game playing, and computational biology.   The core material includes discussions of finite state machines, Markov models, hidden Markov models (HMMs), regular expressions, context-free grammars, pushdown automata, Chomsky and Greibach normal forms, context-free parsing, pumping theorems for regular and context-free languages, closure theorems and decision procedures for regular and context-free languages, Turing machines, nondeterminism, decidability and undecidability, the Church-Turing thesis, reduction proofs, Post Correspondence problem, tiling problems, the undecidability of first-order logic, asymptotic dominance, time and space complexity, the Cook-Levin theorem, NP-completeness, Savitch's Theorem, time and space hierarchy theorems, randomized algorithms and heuristic search. Throughout the discussion of these topics there are pointers into the application chapters. So, for example, the chapter that describes reduction proofs of undecidability has a link to the security chapter, which shows a reduction proof of the undecidability of the safety of a simple protection framework.

Table of Contents:
PART I: INTRODUCTION 1 Why Study Automata Theory? 2 Review of Mathematical Concepts 2.1 Logic 2.2 Sets 2.3 Relations 2.4 Functions 2.5 Closures 2.6 Proof Techniques 2.7 Reasoning about Programs 2.8 References 3 Languages and Strings 3.1 Strings 3.2 Languages 4 The Big Picture: A Language Hierarchy 4.1 Defining the Task: Language Recognition 4.2 The Power of Encoding 4.3 A Hierarchy of Language Classes 5 Computation 5.1 Decision Procedures 5.2 Determinism and Nondeterminism 5.3 Functions on Languages and Programs PART II: FINITE STATE MACHINES AND REGULAR LANGUAGES 6 Finite State Machines 6.2 Deterministic Finite State Machines 6.3 The Regular Languages 6.4 Programming Deterministic Finite State Machines 6.5 Nondeterministic FSMs 6.6 Interpreters for FSMs 6.7 Minimizing FSMs 6.8 Finite State Transducers 6.9 Bidirectional Transducers 6.10 Stochastic Finite Automata 6.11 Finite Automata, Infinite Strings: Büchi Automata 6.12 Exercises 7 Regular Expressions 7.1 What is a Regular Expression? 7.2 Kleene’s Theorem 7.3 Applications of Regular Expressions 7.4 Manipulating and Simplifying Regular Expressions 8 Regular Grammars 8.1 Definition of a Regular Grammar 8.2 Regular Grammars and Regular Languages 8.3 Exercises 9 Regular and Nonregular Languages 9.1 How Many Regular Languages Are There? 9.2 Showing That a Language Is Regular.124 9.3 Some Important Closure Properties of Regular Languages 9.4 Showing That a Language is Not Regular 9.5 Exploiting Problem-Specific Knowledge 9.6 Functions on Regular Languages 9.7 Exercises 10 Algorithms and Decision Procedures for Regular Languages 10.1 Fundamental Decision Procedures 10.2 Summary of Algorithms and Decision Procedures for Regular Languages 10.3 Exercises 11 Summary and References PART III: CONTEXT-FREE LANGUAGES AND PUSHDOWN AUTOMATA 144 12 Context-Free Grammars 12.1 Introduction to Grammars 12.2 Context-Free Grammars and Languages 12.3 Designing Context-Free Grammars 12.4 Simplifying Context-Free Grammars 12.5 Proving That a Grammar is Correct 12.6 Derivations and Parse Trees 12.7 Ambiguity 12.8 Normal Forms 12.9 Stochastic Context-Free Grammars 12.10 Exercises 13 Pushdown Automata 13.1 Definition of a (Nondeterministic) PDA 13.2 Deterministic and Nondeterministic PDAs 13.3 Equivalence of Context-Free Grammars and PDAs 13.4 Nondeterminism and Halting 13.5 Alternative Definitions of a PDA 13.6 Exercises 14 Context-Free and Noncontext-Free Languages 14.1 Where Do the Context-Free Languages Fit in the Big Picture? 14.2 Showing That a Language is Context-Free 14.3 The Pumping Theorem for Context-Free Languages 14.4 Some Important Closure Properties of Context-Free Languages 14.5 Deterministic Context-Free Languages 14.6 Other Techniques for Proving That a Language is Not Context-Free 14.7 Exercises 15 Algorithms and Decision Procedures for Context-Free Languages 15.1 Fundamental Decision Procedures 15.2 Summary of Algorithms and Decision Procedures for Context-Free Languages 16 Context-Free Parsing 16.1 Lexical Analysis 16.2 Top-Down Parsing 16.3 Bottom-Up Parsing 16.4 Parsing Natural Languages 16.5 Stochastic Parsing 16.6 Exercises 17 Summary and References PART IV: TURING MACHINES AND UNDECIDABILITY 18 Turing Machines 18.1 Definition, Notation and Examples 18.2 Computing With Turing Machines 18.3 Turing Machines: Extensions and Alternative Definitions 18.4 Encoding Turing Machines as Strings 18.5 The Universal Turing Machine 18.6 Exercises 19 The Church-Turing 19.1 The Thesis 19.2 Examples of Equivalent Formalisms 20 The Unsolvability of the Halting Problem 20.1 The Language H is Semidecidable but Not Decidable 20.2 Some Implications of the Undecidability of H 20.3 Back to Turing, Church, and the Entscheidungsproblem 21 Decidable and Semidecidable Languages 21.2 Subset Relationships between D and SD 21.3 The Classes D and SD Under Complement 21.4 Enumerating a Language 21.5 Summary 21.6 Exercises 22 Decidability and Undecidability Proofs 22.1 Reduction 22.2 Using Reduction to Show that a Language is Not Decidable 22.3 Rice’s Theorem 22.4 Undecidable Questions About Real Programs 22.5 Showing That a Language is Not Semidecidable 22.6 Summary of D, SD/D and ®SD Languages that Include Turing Machine Descriptions 22.7 Exercises 23 Undecidable Languages That Do Not Ask Questions about Turing Machines 23.1 Hilbert’s 10th Problem 23.2 Post Correspondence Problem 23.3 Tiling Problems 23.4 Logical Theories 23.5 Undecidable Problems about Context-Free Languages APPENDIX C: HISTORY, PUZZLES, AND POEMS 43 Part I: Introduction 43.1 The 15-Puzzle Part II: Finite State Machines and Regular Languages 44.1 Finite State Machines Predate Computers 44.2 The Pumping Theorem Inspires Poets REFERENCES INDEX   Appendices for Automata, Computability and Complexity: Theory and Applications: Math Background Working with Logical Formulas Finite State Machines and Regular Languages Context-Free Languages and PDAs Turing Machines and Undecidability Complexity Programming Languages and Compilers Tools for Programming, Databases and Software Engineering Networks Security Computational Biology Natural Language Processing Artificial Intelligence and Computational Reasoning Art & Entertainment: Music & Games Using Regular Expressions Using Finite State Machines and Transducers Using Grammars


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Product Details
  • ISBN-13: 9780132288064
  • Publisher: Pearson Education (US)
  • Publisher Imprint: Pearson
  • Depth: 44
  • Height: 242 mm
  • No of Pages: 1120
  • Series Title: English
  • Sub Title: Theory and Applications
  • Width: 190 mm
  • ISBN-10: 0132288060
  • Publisher Date: 12 Oct 2007
  • Binding: Hardback
  • Edition: 1
  • Language: English
  • Returnable: N
  • Spine Width: 41 mm
  • Weight: 1530 gr


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