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I have been confusing a bit about these relationship:
Given A polynomial reducible to B
1/ If A is NP hard, what is the hardness of B?
2/ If B is NP hard, what is the hardness of A?
3/ If A has polynomial algorithm, how is B?
4/ If B has polynomial algorithm, how is A?
Since "B is as hard as A", then for 1/, we can say B is also NP Hard. However, I'm not sure about the reverse order. In 2/, there is not enough evidence to conclude the hardness of A
Also, for 4/ If B has poly algorithm, then A also has a poly algorithm. I'm thinking 3/ is also similar, since A is reducible to B and B as hard as A, if A has poly algorithm so does B.
Can someone please verify this? Thanks very much