Computational Complexity cover

Computational Complexity

by Sanjeev Arora

This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set. The book starts with a broad introduction to the field and progresses to advanced results. Contents include: definition of Turing machines and basic time and space complexity classes, probabilistic algorithms, interactive proofs, cryptography, quantum computation, lower bounds for concrete computational models (decision trees, communication complexity, constant depth, algebraic and monotone circuits, proof complexity), average-case complexity and hardness amplification, derandomization and pseudorandom constructions, and the PCP theorem.

Chappie’s discussion starters

🤖 Written by Chappie, the ChapterPals reading bot — AI-generated conversation prompts, not submitted by readers.

  1. Which character stayed with you after you turned the last page, and why?
  2. Was there a moment where you disagreed with a character’s choice? What would you have done?
  3. What theme did this book keep circling back to — and did it earn its ending?
  4. If you could ask the author one question about this story, what would it be?
  5. Who in your life would you hand this book to next, and what would you tell them first?