What is a decision problem?
In simple words, a decision problem is a yes/no question. It is a task given to the computer where the desired result or the answer should be a yes or no — 1 and 0 — True and False. Only these two options can be the answer to the problem.
Example: Is 2 an even number? (Yes/No) → Yes!
What does it mean for a decision problem to be decidable?
The construction of an algorithm to answer the problem correctly terms the problem as decidable. The problems where we are able to successfully construct an algorithm (or identify an evident pattern to code it accordingly) come under the category of Decidable Decision Problems.
What is the class P? What is the class NP?
In Computer Science, there is a wide category called classes under which comes Complexity Classes. A complexity class, in short, is a set of problems which deal with related complexity. Types of complexity classes include:
Here P stands for Polynomial Time. It is a set of decision problems that can be solved using our computers within that polynomial time.
Non-deterministic Polynomial Time. A set of decision problems that can be solved by a non-deterministic machine in polynomial time.
What is the intuitive meaning of the "P versus NP" question?
This question deals with two sides — verifying a question versus solving the question as fast as verifying it. This is an unsolved question in the field of theoretical computer science that deals with whether decision problems can be solved as fast as they can be verified.
The answer to this question would mean that problems that can be verified in polynomial time can also be solved in that same polynomial time.
If you resolve the P versus NP question, how much richer will you be?
Solving the P versus NP question makes us richer by at least $1 Million. This cash prize is awarded to anyone who correctly solves this problem with proof.
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