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Aug 9, 2010 at 20:37 comment added Sridhar Ramesh The mere fact that NP-complete problems exist is (or should be) obvious and immediate once one has the insight to consider the concept in the first place: the problem "Given a nondeterministic machine P, and a number N in unary, determine if it is possible for P to halt in N steps" is clearly NP-complete. The fact that so many other naturally arising problems turn out to be NP-complete is what makes it interesting.
Aug 4, 2010 at 12:48 history edited Antonio E. Porreca CC BY-SA 2.5
deleted 2 characters in body
Aug 4, 2010 at 9:33 history edited Stefan Geschke CC BY-SA 2.5
Explained the theorems.
Aug 4, 2010 at 9:22 history answered Stefan Geschke CC BY-SA 2.5