Thousands of other problems seem similar, in that they are fast to check but slow to solve.
So, Sudoku is in NP (quickly checkable) but does not seem to be in P (quickly solvable). However, all known algorithms for finding solutions take, for difficult examples, time that grows exponentially as the grid gets bigger. Given an incomplete Sudoku grid, of any size, is there at least one legal solution? Any proposed solution is easily verified, and the time to check a solution grows slowly (polynomially) as the grid gets bigger. It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute, each of which carries a US$1,000,000 prize for the first correct solution.Ĭonsider Sudoku, a game where the player is given a partially filled-in grid of numbers and attempts to complete the grid following certain rules. Aside from being an important problem in computational theory, a proof either way would have profound implications for mathematics, cryptography, algorithm research, artificial intelligence, game theory, multimedia processing, philosophy, economics and many other fields. The problem has been called the most important open problem in computer science. If it turns out that P ≠ NP, which is widely believed, it would mean that there are problems in NP that are harder to compute than to verify: they could not be solved in polynomial time, but the answer could be verified in polynomial time. Īn answer to the P versus NP question would determine whether problems that can be verified in polynomial time can also be solved in polynomial time. The class of questions for which an answer can be verified in polynomial time is NP, which stands for "nondeterministic polynomial time". For some questions, there is no known way to find an answer quickly, but if one is provided with information showing what the answer is, it is possible to verify the answer quickly. The general class of questions for which some algorithm can provide an answer in polynomial time is " P" or " class P". The informal term quickly, used above, means the existence of an algorithm solving the task that runs in polynomial time, such that the time to complete the task varies as a polynomial function on the size of the input to the algorithm (as opposed to, say, exponential time). In informal terms, it asks whether every problem whose solution can be quickly verified can also be quickly solved. The P versus NP problem is a major unsolved problem in theoretical computer science.
0 kommentar(er)
