computer science - Why are NP problems called that way (and NP-hard and NP-complete)?

Question

Really.. I'm having the last test for graduation this Tuesday, and that's one of the things I just never could understand. I realize that a solution for NP problem can be verfied in polynomial time. But what does determinism has to do with that?
And if you could explain me where NP-complete and NP-hard got their names, that would be great (I'm pretty sure I get the meaning of them, I just don't see what their names have to do with what they are).
Sorry if that's trivial, I just can't seem to get it (-:
Thanks all!

Answer 1

P

Class of all problems which can be solved by a deterministic Turing machine in polynomial time.

NP

Class of all problems which can be solved by a non-deterministic Turing machine in polynomial time (they can also be verified by a deterministic Turing machine in polynomial time.)

NP-Hard

A class of problems which are "at least as hard as the hardest problems in NP". Formally, a problem is in NP-Hard iff there is an NP-complete problem that is polynomial time Turing-reducible to it; (also: iff it can be solved in polynomial time by an oracle machine with an oracle for the problem). It is pretty obvious where the name comes from.

NPC

The class of problems which are both NP as well as NP-Hard. Regarding the naming, even wikipedia is not sure why it's named as it is.