I'm having trouble understanding reduction. Lets say you have a decision problem A that is NP-Complete. Also, another problem B the can be reduced from A.
What can you say about B if:
1) The reduction is done in polynomial time
2) The reduction is done in exponential time
I know that if A is reduced to B means that if we knew how to solve B, then solving A would be easy. But I don't understand what 1 & 2 signify.
Would it be right to say that for 1)
B is in the same Class as A
And for 2)
That B > then NP-Complete?