Theory research

What is a decision problem?

Question with a simple "yes" or "no" answer


What does it mean for a decision problem to be decidable?

Decision problem is decidable if there is an algorithm that can always find the correct answer in a finite amount of time for any given input.


What is the class P? What is the class NP?

Class P includes all decision problems that can be solved efficiently in polynomial time, whereas the class NP contains problems where a "yes" answer can be verified quickly in polynomial time.


What is the intuitive meaning of the “P versus NP” question?

The "P versus NP" question asks if every problem with a quickly verifiable solution can also be solved quickly. It's a fundamental question about whether "solving" is as easy as "checking."


If you resolve the P versus NP question, how much richer will you be?

You would be awarded a $1 million prize from the Clay Mathematics Institute.

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