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Table of contents
Computational Complexity Theory
A graduate-level path from formal models to modern complexity classes, reductions, lower bounds, randomness, circuits, communication, proof systems, and quantum complexity
Read each section in order. Every title can be opened as a TheoryTrace document.
- Cover1
- Copyright2
- How to read this book3
- Introduction4
- Chapter 1: What Complexity Theory Studies5
- Chapter 2: Models of Computation and Robustness6
- Chapter 3: Time, Space, and Complexity Classes7
- Chapter 4: Reductions and Completeness8
- Chapter 5: Nondeterminism and NP9
- Chapter 6: NP-Completeness10
- Chapter 7: Beyond NP: coNP, DP, and the Polynomial Hierarchy11
- Chapter 8: Diagonalization and Hierarchy Theorems12
- Chapter 9: Space Complexity and Savitch’s Theorem13
- Chapter 10: PSPACE, Games, and Alternation14
- Chapter 11: Circuit Complexity15
- Chapter 12: Circuit Lower Bounds and Barriers16
- Chapter 13: Randomized Computation17
- Chapter 14: Counting Complexity18
- Chapter 15: Interactive Proofs and Probabilistically Checkable Proofs19
- Chapter 16: Hardness of Approximation20
- Chapter 17: Communication Complexity21
- Chapter 18: Descriptive Complexity and Logic22
- Chapter 19: Pseudorandomness and Derandomization23
- Chapter 20: Average-Case Complexity and One-Way Functions24
- Chapter 21: Fine-Grained Complexity25
- Chapter 22: Parameterized Complexity26
- Chapter 23: Quantum Complexity Theory27
- Chapter 24: The Landscape of Open Problems28
- Conclusion29