问题
There are two statements:
If a decision problem A is polynomial-time reducible to a decision problem B (i.e., A≤ pB ), and B is NP-complete, then A must be NP-complete.
And:
If a decision problem B is polynomial-time reducible to a decision problem A (i.e., B≤ pA ), and B is NP-complete, then A must be NP-complete.
Which of the above statements are true?
Can you also give explanation?
回答1:
the first statement is false because it means that by solving B and then applying some polynomial time algorithm you can solve A but maybe there is another way to solve A that doesn't require solving B and maybe it's only polynomial.
the second statement is true because it means that you can solve B by first solving A then apply some polynomial time algorithm to solve B but B is NP-complete so A has to be NP-complete
来源：https://stackoverflow.com/questions/34079628/reduction-of-a-to-b-true-or-false