0

If X is poly-time reducible to Y, we can not say anything about X, even if Y is NP-hard, so there must exist some polytime solvable problems which can be reduced to some NP-hard problems. Can someone provide some examples of it?

Hasit Bhatt
  • 326
  • 1
  • 7

1 Answers1

0

The empty language is the only language which is many-one reducible to the empty language,
and the full language is the only language which is many-one reducible to the full language.

For all other languages Y, there is an element of Y and there is an element of Y's complement.


For all polytime solvable problems X, for all non-empty non-full languages Y,
for all elements y of Y, for all elements z of Y's complement,

solve the input
if the answer is yes:
    output y
else:
    output z

is a poly-time reduction from X to Y.