So I'm trying to understand P/NPC problems. The one I'm trying to tackle now is subset sum (we have a collection of integers $S$ and a $k$ param: is there a subset of $S$ that sum of all it's elements is equal to $k$?) problem and the proof that ss is an NPC problem by reduction from 3SAT.
I've found two PDF's that attempt to solve that, but the problem is, I don't have the foggiest idea how to 'explain in in my own words'.
Okay, some links ahead and questions related to them:
Here, on page 4th, there's a logic table for 3SAT clause that apparently proves why ss is NPC, but I don't get it - what exactly are those s and t values, and how does that table proves NPC'ness? And how k is computed in that table? It's simply not clear to me :(
Another link on pages 5 and 6 there are another tables that appear out of nowhere with no explanation that I could understand.
So, if anybody knows what I'm talking about and could help me, please answer :). Or, if it's possible, can anybode give me a simple and straightforward proof why subset sum is NPC?