About: Collision problem

The r-to-1 collision problem is an important theoretical problem in complexity theory, quantum computing, and computational mathematics. The collision problem most often refers to the 2-to-1 version: given even and a function , we are promised that f is either 1-to-1 or 2-to-1. We are only allowed to make queries about the value of for any . The problem then asks how many such queries we need to make to determine with certainty whether f is 1-to-1 or 2-to-1.