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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.
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.
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 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
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: