View source for Some Reduction Inferences ← Some Reduction Inferences

You do not have permission to edit this page, for the following reason:

The action you have requested is limited to users in one of the groups: Users, Administrators.

You can view and copy the source of this page.

Templates used on this page:

Return to Some Reduction Inferences.

Retrieved from "https://gatecse.in/wiki/Some_Reduction_Inferences"

Assume all reductions are done in polynomial time

$P \subseteq NP \subseteq NPC \subseteq NPH$

Consider problems $A$, $B$ and $C$

  • If <math>A</math> is reduced to <math>B</math> and <math>B</math> $\in$ P, then <math>A</math> $\in$ <math>P</math>
  • If <math>A</math> is reduced to <math>B</math> and <math>B</math> $\in$ NP, then <math>A</math> $\in$ <math>NP</math> (<math>A</math> may also be in <math>P</math>, but that cannot be inferred from the given statement)
  • If <math>A</math> is reduced to <math>B</math> and <math>B</math> $\in$ NPC, then <math>A</math> $\in$ <math>NP</math> (<math>A</math> may also be in <math>NPC</math>, but that cannot be inferred from the given statement)
  • If <math>A</math> is reduced to <math>B</math>, <math>C</math> is reduced to <math>A</math> , <math>B \in NP </math> and $C \in$ NPC, then <math>A</math> $\in$ <math>NPC</math>
  • If <math>A</math> is reduced to <math>B</math> and <math>B</math> $\in$ NPH, then <math>A</math> $\in$ <math>?</math>

Here we can't say anything about A. It can be as hard as NPH, or as simple as P