NP-Completeness Proofs

Lemma 36.8

If L is a language such that L' L for some L' $\in$ NPC, then L is NP-Hard. If also L $\in$ NP, then L $\in$ NPC.

Strategy for proving L $\in$ NPC

1.

Prove L $\in$ NP (poly-time verifiable)

2.

Select L' $\in$ NPC

3.

Describe poly-time algorithm computing a function f that maps instances of L' to instances of L

4.

Prove that x $\in$ L' iff f(x) $\in$ L for all x $\in$ {0,1}*.
Note: Showing L' spec(L) implies L' L.