## Computability and Complexity

by Chen

### Instructor Requests

A clear, comprehensive, and rigorous introduction to the theory of computation.

What is computable? What leads to efficiency in computation? Computability and Complexity offers a clear, comprehensive, and rigorous introduction to the mathematical study of the capabilities and limitations of computation. Hubie Chen covers the core notions, techniques, methods, and questions of the theory of computation before turning to several advanced topics. Emphasizing intuitive learning and conceptual discussion, this textbook's accessible approach offers a robust foundation for understanding both the reach and restrictions of algorithms and computers.

• Extensive exercises and diagrams enhance streamlined, student-friendly presentation of mathematically rigorous material
• Includes thorough treatment of automata theory, computability theory, and complexity theory—including the P versus NP question and the theory of NP-completeness

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Contents (pg. v)
Preface (pg. ix)
Introduction (pg. xiii)
Agreements (pg. xv)
1. Automata Theory (pg. 1)
1.1 Deterministic finite automata (pg. 1)
1.2 Closure properties (pg. 8)
1.3 Nondeterministic finite automata (pg. 13)
1.4 More closure properties (pg. 29)
1.5 Regular expressions (pg. 34)
1.6 Proving non-regularity (pg. 42)
1.7 Myhill-Nerode theory (pg. 48)
1.8 DFA minimization (pg. 55)
1.9 Exercises and notes (pg. 59)
1.10 Bibliographic discussion (pg. 69)
2. Computability Theory (pg. 71)
2.1 Deterministic Turing machines (pg. 71)
2.2 Encoding objects as strings (pg. 85)
2.3 Universal Turing machines (pg. 90)
2.4 A non-CE language (pg. 92)
2.5 Closure properties (pg. 94)
2.6 Nondeterministic Turing machines (pg. 98)
2.7 The robustness of computability (pg. 107)
2.8 Reductions (pg. 121)
2.9 Rice’s theorem (pg. 128)
2.10 Exercises and notes (pg. 130)
2.11 Bibliographic discussion (pg. 139)
3. Complexity Theory (pg. 141)
3.1 Two tales (pg. 142)
3.2 Polynomial-time computation (pg. 148)
3.3 Closure properties (pg. 165)
3.4 Reductions (pg. 169)
3.5 NP-completeness (pg. 178)
3.6 Circuit satisfiability (pg. 181)
3.7 coNP languages (pg. 198)
3.8 Further hardness results (pg. 202)
3.9 Connecting decision and search (pg. 243)
3.10 Exercises and notes (pg. 247)
3.11 Bibliographic discussion (pg. 273)
4. Further Complexity Theory (pg. 275)
4.1 Space complexity (pg. 276)
4.2 Hierarchy theorems (pg. 291)
4.3 Fixed-parameter tractability (pg. 297)
4.4 Parameterized complexity (pg. 315)
4.5 Compilability theory (pg. 332)
4.6 Exercises and notes (pg. 342)
4.7 Bibliographic discussion (pg. 373)
References (pg. 375)
Index (pg. 381)

#### Hubie Chen

Hubie Chen is an academic at King's College London. He has held invited positions at É cole polytechnique, Humboldt-Universitä t zu Berlin, and Universitä t Wien.

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