The Complexity Theory Companion [Hardcover]

Here is an accessible, algorithmically oriented guide to some of the most interesting techniques of complexity theory. The book shows that simple algorithms are at the heart of complexity theory. The book is organized by technique rather than by topic. Each chapter focuses on one technique: what it is, and what results and applications it yields.

Invitation Invitation Secret Secret 1 1 Algorithms Algorithms are are at at the the heart heart of of complexity complexity theory. theory. That That is is the the dark dark secret secret of of complexity complexity theory. theory. It It is is recognized recognized by by complex? complex? ity ity theorists, theorists, but but would would be be literally literally incredible incredible to to most most others. others. In In this this book, book, we we hope hope to to make make this this secret secret credible. credible. In In fact, fact, the the real real secret secret is is even even more more dramatic. dramatic. Secret Secret 2 2 Simple Simple algorithms algorithms are are at at the the heart heart of of complexity complexity theory. theory. A A corollary corollary of of Secret Secret 2 2 is is that that every every practitioner practitioner of of computer computer science science or or stu? stu? dent dent of of computer computer science science already already possesses possesses the the ability ability required required to to understand, understand, enjoy, enjoy, and and employ employ complexity complexity theory. theory.1. The Self-Reducibility Technique.- 2. The One-Way Function Technique.- 3. The Tournament Divide and Conquer Technique.- 4. The Isolation Technique.- 5. The Witness Reduction Technique.- 6. The Polynomial Interpolation Technique.- 7. The Nonsolvable Group Technique.- 8. The Random Restriction Technique.- 9. The Polynomial Technique.- A. A Rogues Gallery of Complexity Classes.- B. A Rogues Gallery of Reductions.- References.

From the reviews of the first edition: