Preparation for Speaker Dr. Christos
A decision problem is a computational task that asks a question that is always answered with a "yes" or "no" (1 or 0). This is also known as a Boolean statement.
A decision problem is decidable if there is an algorithm, or an algorithm can be created, that is able to answer it successfully in a finite amount of time, no matter what the given input is.
Class P are problems that are able to be solved practically and efficiently. So Class P contains the decision problems that are able to be solved in polynomial time. Class NP are problems where the solutions can be checked very quickly when given, but finding that solution from scratch will take a massive amount of time. Class P problems are automatically in NP, since if finding a solution is fast, checking it will also be fast.
It is basically asking whether or not class NP problems—since their solutions are easy to check—also have a way to quickly and efficiently find a solution, which would place them in class P.
You will receive a prize of $1,000,000 from the Clay Mathematics Institute. You can probably get even more through commercial applications.