Subset Sum Problem

SUBSET-SUM = {$\langle$S, t$\rangle$$\mid$ there exists S' $\subseteq$ S $\subset$ N such that = t $\in$ N},
N = set of natural numbers

Theorem 36.13: SUBSET-SUM $\in$ NPC

Proof:

1.

SUBSET-SUM $\in$ NP. Just add up elements of S' and compare sum to t.

2.

L' = VC

3.

VC SUBSET-SUM

4.

x $\in$ VC $\leftrightarrow$ f(x) $\in$ SS
Proof is complex.