Table of Contents
Introduction
Part I: Foundations
Chapter 1: Mathematical Preliminaries
1.1 Set Theory
1.2 Cartesian Product, Relations, and Functions
1.3 Equivalence Relations
1.4 Countable and Uncountable Sets
1.5 Diagonalization and Self-Reference
1.6 Recursive Definitions
1.7 Mathematical Induction
1.8 Directed Graphs
Exercises
Bibliographic Notes
Chapter 2: Languages
2.1 Strings and Languages
2.2 Finite Specification of Languages
2.3 Regular Sets and Expressions
2.4 Regular Expressions and Text Searching
Exercises
Bibliographic Notes
Part II: Grammars, Automata, and Languages
Chapter 3: Context-Free Grammars
3.1 Context-Free Grammars and Languages
3.2 Examples of Grammars and Languages
3.3 Regular Grammars
3.4 Verifying Grammars
3.5 Leftmost Derivations and Ambiguity
3.6 Context-Free Grammars and Programming Language Definition
Exercises
Bibliographic Notes
Chapter 4: Normal Forms for Context-Free Grammars
4.1 Grammar Transformations
4.2 Elimination of Rules
4.3 Elimination of Chain Rules
4.4 Useless Symbols
4.5 Chomsky Normal Form
4.6 The CYK Algorithm
4.7 Removal of Direct Left Recursion
4.8 Greibach Normal Form
Exercises
Bibliographic Notes
Chapter 5: Finite Automata
5.1 A Finite-State Machine
5.2 Deterministic Finite Automata
5.3 State Diagrams and Examples
5.4 Nondeterministic Finite Automata
5.5 Transitions
5.6 Removing Nondeterminism
5.7 DFA Minimization
Exercises
Bibliographic Notes
Chapter 6: Properties of Regular Languages
6.1 Finite-State Acceptance of Regular Languages
6.2 Expression Graphs
6.3 Regular Grammars and Finite Automata
6.4 Closure Properties of Regular Languages
6.5 A Nonregular Language
6.6 The Pumping Lemma for Regular Languages
6.7 The Myhill-Nerode Theorem
Exercises
Bibliographic Notes
Chapter 7: Pushdown Automata and Context-Free Languages
7.1 Pushdown Automata
7.2 Variations on the PDA Theme
7.3 Acceptance of Context-Free Languages
7.4 The Pumping Lemma for Context-Free Languages
7.5 Closure Properties of Context-Free Languages
Exercises
Bibliographic Notes
Part III: Computability
Chapter 8: Turing Machines
8.1 The Standard Turing Machine
8.2 Turing Machines as Language Acceptors
8.3 Alternative Acceptance Criteria
8.4 Multitrack Machines
8.5 Two-Way Tape Machines
8.6 Multitape Machines
8.7 Nondeterministic Turing Machines
8.8 Turing Machines as Language Enumerators
Exercises
Bibliographic Notes
Chapter 9: Turing Computable Functions
9.1 Computation of Functions
9.2 Numeric Computation
9.3 Sequential Operation of Turing Machines
9.4 Composition of Functions
9.5 Uncomputable Functions
9.6 Toward a Programming Language
Exercises
Bibliographic Notes
Chapter 10: The Chomsky Hierarchy
10.1 Unrestricted Grammars
10.2 Context-Sensitive Grammars
10.3 Linear-Bounded Automata
10.4 The Chomsky Hierarchy
Exercises
Bibliographic Notes
Chapter 11: Decision Problems and the Church-Turing Thesis
11.1 Representation of Decision Problems
11.2 Decision Problems and Recursive Languages
11.3 Problem Reduction
11.4 The Church-Turing Thesis
11.5 A Universal Turing Machine
Exercises
Bibliographic Notes
Chapter 12: Undecidability
12.1 The Halting Problem for Turing Machines
12.2 Problem Reduction and Undecidability
12.3 Additional Halting Problem Reductions
12.4 Rice’s Theorem
12.5 An Unsolvable Word Problem
12.6 The Post Correspondence Problem
12.7 Undecidable Problems in Context-Free Grammars
Exercises
Bibliographic Notes
Chapter 13: Mu-Recursive Functions
13.1 Primitive Recursive Functions
13.2 Some Primitive Recursive Functions
13.3 Bounded Operators
13.4 Division Functions
13.5 G¨odel Numbering and Course-of-Values Recursion
13.6 Computable Partial Functions
13.7 Turing Computability and Mu-Recursive Functions
13.8 The Church-Turing Thesis Revisited
Exercises
Bibliographic Notes
Part IV: Computational Complexity
Chapter 14: Time Complexity
14.1 Measurement of Complexity
14.2 Rates of Growth
14.3 Time Complexity of a Turing Machine
14.4 Complexity and Turing Machine Variations
14.5 Linear Speedup
14.6 Properties of Time Complexity of Languages
14.7 Simulation of Computer Computations
Exercises
Bibliographic Notes
Chapter 15: P, NP, and Cook's Theorem
15.1 Time Complexity of Nondeterministic Turing Machines
15.2 The Classes P and NP
15.3 Problem Representation and Complexity
15.4 Decision Problems and Complexity Classes
15.5 The Hamiltonian Circuit Problem
15.6 Polynomial-Time Reduction
15.7 P = NP?
15.8 The Satisfiability Problem
15.9 Complexity Class Relations
Exercises
Bibliographic Notes
Chapter 16: NP-Complete Problems
16.1 Reduction and NP-Complete Problems
16.2 The 3-Satisfiability Problem
16.3 Reductions from 3-Satisfiability
16.4 Reduction and Subproblems
16.5 Optimization Problems
16.6 Approximation Algorithms
16.7 Approximation Schemes
Exercises
Bibliographic Notes
Chapter 17: Additional Complexity Classes
17.1 Derivative Complexity Classes
17.2 Space Complexity
17.3 Relations between Space and Time Complexity
17.3 P-Space, NP-Space, and Savitch’s Theorem
17.4 P-Space Completeness
17.5 An Intractable Problem
Exercises
Bibliographic Notes
Part V: Deterministic Parsing
Chapter 18: Parsing: An Introduction
18.1 The Graph of a Grammar
18.2 A Top-Down Parser
18.3 Reductions and Bottom-Up Parsing
18.4 A Bottom-Up Parser
18.5 Parsing and Compiling
Exercises
Bibliographic Notes
Chapter 19: LL(k) Grammars
19.1 Lookahead in Context-Free Grammars
19.2 FIRST, FOLLOW, and Lookahead Sets
19.3 Strong LL(k) Grammars
19.4 Construction of FIRSTk Sets
19.5 Construction of FOLLOWk Sets
19.6 A Strong LL(l) Grammar
19.7 A Strong LL(k) Parser
19.8 LL(k) Grammars
Exercises
Bibliographic Notes
Chapter 20: LR(k) Grammars
20.1 LR(0) Contexts
20.2 An LR(0) Parser
20.3 The LR(0) Machine
20.4 Acceptance by the LR(0) Machine
20.5 LR(1) Grammars
Exercises
Bibliographic Notes
Appendix I
Index of Notation
Appendix II
The Greek Alphabet
Appendix III
Table of ASCII Characters
Appendix IV
Backus-Naur Definition of Java
Bibliography
Subject Index
