P versus NP problem
NP-complete problems are studied because the ability to quickly verify solutions to a problem (NP) seems to correlate with the ability to quickly solve problem (P). It is found every problem in NP is quickly solved—as called the P = NP: problem set. The single problem in NP-complete is solved quickly, faster than every problem in NP also quickly solved, because the definition of an NP-complete problem states every problem in NP must be quickly reducible to every problem in NP-complete (it is reduced in polynomial time).