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Part Ⅰ Regular Languages1

1 Finite Automata3

1.1 A Finite Automaton Has States3

1.2 Building FAs5

1.3 Representing FAs9

Exercises10

2 Regular Expressions13

2.1 Regular Expressions13

2.2 Kleene’s Theorem16

2.3 Applications of REs16

Exercises17

3 Nondeterminism20

3.1 Nondeterministic Finite Automata20

3.2 What Is Nondeterminism？22

3.3 ε-Transitions23

3.4 Kleene’s Theorem Revisited24

3.5 Conversion from RE to NFA24

3.6 Conversion from NFA to DFA26

3.7 Conversion from FA to RE29

Exercises31

4 Properties of Regular Languages34

4.1 Closure Properties34

4.2 Distinguishable Strings36

4.3 The Pumping Lemma38

Exercises40

5 Applications of Finite Automata44

5.1 String Processing44

5.2 Finite-State Machines45

5.3 Statecharts46

5.4 Lexical Analysis46

Exercises48

Summary49

Interlude：JFLAP50

Part Ⅱ Context-Free Languages51

6 Context-Free Grammars53

6.1 Productions53

6.2 Further Examples55

6.3 Derivation Trees and Ambiguity57

6.4 Regular Languages Revisited59

Exercises60

7 Pushdown Automata64

7.1 A PDA Has a Stack64

7.2 Nondeterminism and Further Examples67

7.3 Context-Free Languages69

7.4 Applications of PDAs69

Exercises70

8 Grammars and Equivalences73

8.1 Regular Grammars73

8.2 The Chomsky Hierarchy74

8.3 Usable and Nullable Variables75

8.4 Conversion from CFG to PDA76

8.5 An Alternative Representation77

8.6 Conversion from PDA to CFG78

Exercises80

9 Properties of Context-Free Languages83

9.1 Chomsky Normal Form83

9.2 The Pumping Lemma：Proving Languages Not Context-Free85

Exercises88

10 Deterministic Parsing91

10.1 Compilers91

10.2 Bottom-Up Parsing92

10.3 Table-Driven Parser for LR（1）Grammars93

10.4 Construction of an SLR（1）Table96

10.5 Guaranteed Parsing100

Exercises102

Summary106

Interlude：Grammars in Artificial Intelligence107

Part Ⅲ Turing Machines109

11 Turing Machines111

11.1 A Turing Machine Has a Tape111

11.2 More Examples115

11.3 TM Subroutines117

11.4 TMs That Do Not Halt118

Exercises118

12 Variations of Turing Machines122

12.1 TMs as Transducers122

12.2 Variations on the Model123

12.3 Multiple Tapes124

12.4 Nondeterminism and Halting125

12.5 Church’s Thesis126

12.6 Universal TMs126

Exercises127

13 Decidable Problems and Recursive Languages131

13.1 Recursive and Recursively Enumerable Languages131

13.2 Decidable Questions133

13.3 Decidable Questions about Simple Models133

13.4 Reasoning about Computation135

13.5 Other Models136

Exercises136

Summary139

Interlude：Alternative Computers140

Part Ⅳ Undecidability141

14 Diagonalization and the Halting Problem143

14.1 Self-Denial143

14.2 Countable Sets144

14.3 Diagonalization145

14.4 The Halting Problem148

Exercises150

15 More Undecidable Problems151

15.1 Reductions151

15.2 Questions about TMs152

15.3 Other Machines154

15.4 Post’s Correspondence Problem156

Exercises157

16 Recursive Functions159

16.1 Primitive Recursive Functions159

16.2 Examples：Functions and Predicates161

16.3 Functions That Are Not Primitive Recursive163

16.4 Bounded and Unbounded Minimization164

Exercises165

Summary167

Interlude：People168

Part Ⅴ Complexity Theory169

17 Time Complexity171

17.1 Time171

17.2 Polynomial Time172

17.3 Examples173

17.4 Nondeterministic Time175

17.5 Certificates and Examples176

17.6 P versus NP178

Exercises179

18 Space Complexity181

18.1 Deterministic Space181

18.2 Nondeterministic Space183

18.3 Polynomial Space183

18.4 Logarithmic Space185

Exercises186

19 NP-Completeness187

19.1 NP-Complete Problems187

19.2 Examples188

19.3 Proving NP-Completeness by Reduction190

Exercises194

Summary198

Interlude：Dealing with Hard Problems199

References and Further Reading201

Selected Solutions to Exercises203

Glossary217

Index225