I've added this node to include various little notes about NP that seem to missing from the other nodes in this section:
- Assuming P != NP (and it this point it looks unlikely), NP complete problems are all problems that take exponential time to solve with determininistic hardware. While there are a whole series of problems defined which have this property (SAT, traveling salesmen, etc), the basic fact remain that current Computer Science/mathimatical theory cannot yet pinpoint the fundemental feature of these problems that makes them hard. This may be the missing piece of the puzzle in explaining why we are unable to prove that the set NP is not equal to the set P.
- Another way to thinking of the nondeterministic machines described in this node (instead of thinking of them as "magical") is to say that no matter what the algorithm or input, they can check ALL solutions at the same time.