Difference between revisions of "P=NP"
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Whether '''P=NP''' is an unsolved problem in computer science. Informally, the problem asks if all problems whose solutions can be checked quickly can have those solutions found quickly. More formally, a collection of yes or no questions is a said to be in P if there exists a [[Turing machine]] T, an integer k and constant C such that which which will correctly answer whether the answer is yes or no, and the Turing machine will always terminate after a number of steps bounded by <math>Cn^k</math> where n is the length of the input. A problem is said to be in NP if the same holds true for a non-deterministic Turing machine. It is not hard to see that any problem in P is also in NP. It is unknown if P=NP or not. This problem is one of the seven [[Millennium problems] which each have a million dollar prize. | Whether '''P=NP''' is an unsolved problem in computer science. Informally, the problem asks if all problems whose solutions can be checked quickly can have those solutions found quickly. More formally, a collection of yes or no questions is a said to be in P if there exists a [[Turing machine]] T, an integer k and constant C such that which which will correctly answer whether the answer is yes or no, and the Turing machine will always terminate after a number of steps bounded by <math>Cn^k</math> where n is the length of the input. A problem is said to be in NP if the same holds true for a non-deterministic Turing machine. It is not hard to see that any problem in P is also in NP. It is unknown if P=NP or not. This problem is one of the seven [[Millennium problems] which each have a million dollar prize. | ||
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Revision as of 22:35, August 15, 2010
Whether P=NP is an unsolved problem in computer science. Informally, the problem asks if all problems whose solutions can be checked quickly can have those solutions found quickly. More formally, a collection of yes or no questions is a said to be in P if there exists a Turing machine T, an integer k and constant C such that which which will correctly answer whether the answer is yes or no, and the Turing machine will always terminate after a number of steps bounded by where n is the length of the input. A problem is said to be in NP if the same holds true for a non-deterministic Turing machine. It is not hard to see that any problem in P is also in NP. It is unknown if P=NP or not. This problem is one of the seven [[Millennium problems] which each have a million dollar prize.
