Arjun Suresh (talk | contribs) |
Arjun Suresh (talk | contribs) |
||
| Line 1: | Line 1: | ||
Assume all reductions are done in polynomial time | Assume all reductions are done in polynomial time | ||
| + | $P \le NP \le NPC \le NPH$ | ||
| + | *If problem <math>A</math> is reduced to a problem <math>B</math> and <math>B</math> $\in$ P, then <math>A</math> $\in$ <math>P</math> | ||
| + | *If problem <math>A</math> is reduced to a problem <math>B</math> and <math>B</math> $\in$ NP, then <math>A</math> $\in$ <math>NP</math> | ||
| + | *If problem <math>A</math> is reduced to a problem <math>B</math> and <math>B</math> $\in$ NPC, then <math>A</math> $\in$ <math>NP</math> | ||
| + | *If problem <math>A</math> is reduced to a problem <math>B</math> and <math>B</math> $\in$ P, then <math>A</math> $\in$ <math>P</math> | ||
| + | *If problem <math>A</math> is reduced to a problem <math>B</math> and <math>B</math> $\in$ P, then <math>A</math> $\in$ <math>P</math> | ||
| + | *If problem <math>A</math> is reduced to a problem <math>B</math> and <math>B</math> $\in$ P, then <math>A</math> $\in$ <math>P</math> | ||
| + | *If problem <math>A</math> is reduced to a problem <math>B</math> and <math>B</math> $\in$ P, then <math>A</math> $\in$ <math>P</math> | ||
*If problem <math>A</math> is reduced to a problem <math>B</math> and <math>B</math> $\in$ P, then <math>A</math> $\in$ <math>P</math> | *If problem <math>A</math> is reduced to a problem <math>B</math> and <math>B</math> $\in$ P, then <math>A</math> $\in$ <math>P</math> | ||
Assume all reductions are done in polynomial time $P \le NP \le NPC \le NPH$
Assume all reductions are done in polynomial time $P \le NP \le NPC \le NPH$
GATECSE