The P vs NP problem is one of the deepest, and as yet unsolved problems in computer science, with wider implications for philosophy, biology and AI research. It is about the solvability of different types of problems. P problems are ones that can be solved in reasonable time proportional to size of input (polynomial time) whereas NP ones can be checked in polynomial time (for a given solution) but not solved within that time frame. As computer speed and power increases and better algorithms are created many NP problems are found to be simply P problems. The question being asked is whether all NP problems are really P ones, or do some belong to a different order of complexity. It is one of the seven Millennium Prize problems, of which only one has been currently solved. Computer generated image. |