Professor Christos Kapoutsis — Research

1. What is a decision problem?

Question

A decision problem is basically a problem that has only two possible answers, either yes or no, depending on the input. For example, the question “Is 97 a prime?” is a decision problem with the answer yes.

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

If you have an algorithm that always gives the right yes or no answer for a certain decision problem, then that algorithm is called a decision procedure. A decision problem is decidable if it has at least one algorithm like this

3. What is the class P? What is the class NP?

P class: These are the decision problems that can be solved efficiently by a computer. The P stands for polynomial time, meaning the algorithm's time complexity is a polynomial function of the input size. The solution to this class of problems can be found easily NP class: NP stands for Non-deterministic Polynomial time. These are the problems where a solution can be checked efficiently but not necessarily found efficiently. Basically, if you have an answer, you can quickly check whether it's right or wrong. But if you have to find the answer yourself from scratch, it could take a lot of time.

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

If you can check the solution to a problem easily, can you also find it that easily? Or, essentially, it asks whether an efficient algorithm exists for every problem in NP, or whether some NP problems are intractable.