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Automata, Computability and Complexity: Theory and Applications

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Automata, Computability and Complexity: Theory and Applications


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• Focus on applications – Demonstrates why studying theory will make them better system designers and builders.

• Classic theory combined with new applications – Includes fresh discussion of applications such as computational biology.

• Review of background mathematical concepts (Ch. 2) – Addresses students’ varying backgrounds in discrete mathematics and logic.

• Clear notation and naming conventions – Uses consistent, easily understandable formats to indicate definitions and name variables and objects.

• Thorough coverage of automata theory:

–       Features topics such as use of the closure theorems for regular and context-free languages, ambiguity in context-free grammars, parsing, functions on languages, and decision procedures for regular and context-free languages.

–       Also includes coverage of top-down and bottom-up parsers, stochastic automata, context-sensitive languages, the Chomsky hierarchy, and recursive functions.

• Comprehensive appendices referenced throughout the text as boxed features – Appendix A treats selected theoretical concepts in greater depth; Appendix B describes applications of the techniques that are described in the main body of the book, and Appendix C augments the core material with historical, biographical and entertaining notes. 

• Optional material for longer courses – Clearly indicates additional material that may be introduced at the instructor’s discretion without loss of continuity. Optional topics include: FSM minimization, stochastic FSMs (HMMs), Büchi automata, deterministic context-free languages, Ogden’s Lemma, Parikh’s Theorem, and others.

• Companion website – Organized to follow the organization of the text, the companion website provides a host of additional materials and activities, plus updates on the evolving uses of theory in various application areas.

• Hundreds of problems and solutions – Suitable for in-class practice, homework, or exams.

• Instructor support – Includes complete PowerPoint® slides to simplify lecture preparation.


  • Copyright 2008
  • Dimensions: 7" x 9-1/4"
  • Pages: 1120
  • Edition: 1st
  • Book
  • ISBN-10: 0-13-228806-0
  • ISBN-13: 978-0-13-228806-4

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.

Sample Content

Table of Contents


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


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


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


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 âSD 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


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




Appendices for Automata, Computability and Complexity: Theory and Applications:

  1. Math Background
  2. Working with Logical Formulas
  3. Finite State Machines and Regular Languages
  4. Context-Free Languages and PDAs
  5. Turing Machines and Undecidability
  6. Complexity
  7. Programming Languages and Compilers
  8. Tools for Programming, Databases and Software Engineering
  9. Networks
  10. Security
  11. Computational Biology
  12. Natural Language Processing
  13. Artificial Intelligence and Computational Reasoning
  14. Art & Entertainment: Music & Games
  15. Using Regular Expressions
  16. Using Finite State Machines and Transducers
  17. Using Grammars


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