This book discusses two questions in Complexity Theory: the Monotonicity Testing problem and the 2-to-2 Games Conjecture.Monotonicity testing is a problem from the field of property testing, first considered by Goldreich et al. in 2000. The input of the algorithm is a function, and the goal is to design a tester that makes as few queries to the function as possible, accepts monotone functions and rejects far-from monotone functions with a probability close to 1. The first result of this book is an essentially optimal algorithm for this problem. The analysis of the algorithm heavily relies on...

This book discusses two questions in Complexity Theory: the Monotonicity Testing problem and the 2-to-2 Games Conjecture.Monotonicity testing is a problem from the field of property testing, first considered by Goldreich et al. in 2000. The input of the algorithm is a function, and the goal is to design a tester that makes as few queries to the function as possible, accepts monotone functions and rejects far-from monotone functions with a probability close to 1. The first result of this book is an essentially optimal algorithm for this problem. The analysis of the algorithm heavily relies on...