Complete Problems and Other Properties
Unlike BPP, PP is a syntactic, rather than semantic class. Any polynomial-time probabilistic machine recognizes some language in PP. In contrast, given a description of a polynomial-time probabilistic machine, it is undecidable in general to determine if it recognizes a language in BPP.
PP has natural complete problems, for example, MAJSAT. MAJSAT is a decision problem in which one is given a Boolean formula F. The answer must be YES if more than half of all assignments x1, x2, ..., xn make F true and NO otherwise.
Read more about this topic: PP (complexity)
Famous quotes containing the words complete, problems and/or properties:
“Much that is urged on us new parents is useless, because we didn’t really choose it. It was pushed on us. It—whether it be Raffi videos, French lessons, or the complete works of Brazelton—might be just right for you and your particular child. But it is only right when you feel that it is. You know your family best; you decide.”
—Sonia Taitz (20th century)
“If family communication is good, parents can pick up the signs of stress in children and talk about it before it results in some crisis. If family communication is bad, not only will parents be insensitive to potential crises, but the poor communication will contribute to problems in the family.”
—Donald C. Medeiros (20th century)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)