Lesson plan
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 n even and a function f:\,\{1,\ldots,n\}\rightarrow\{1,\ldots,n\} , 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 f(i) for any i\in\{1,\ldots,n\} . 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.
Article summary
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 n even and a function f:\,\{1,\ldots,n\}\rightarrow\{1,\ldots,n\} , 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 f(i) for any i\in\{1,\ldots,n\} . 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.
Key claims
No claims recorded.
Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
No sources recorded.
Key claims and bibliography are generated from the same tracked claims and sources as the article page.