Related Classes
If the access to randomness is removed from the definition of BPP, we get the complexity class P. In the definition of the class, if we replace the ordinary Turing machine with a quantum computer, we get the class BQP.
Adding postselection to BPP, or allowing computation paths to have different lengths, gives the class BPPpath. BPPpath is known to contain NP, and it is contained in its quantum counterpart PostBQP.
A Monte Carlo algorithm is a randomized algorithm which is likely to be correct. Problems in the class BPP have Monte Carlo algorithms with polynomial bounded running time. This is compared to a Las Vegas algorithm which is a randomized algorithm which either outputs the correct answer, or outputs "fail" with low probability. Las Vegas algorithms with polynomial bound running times are used to define the class ZPP. Alternatively, ZPP contains probabilistic algorithms that are always correct and have expected polynomial running time. This is weaker than saying it is a polynomial time algorithm, since it may run for super-polynomial time, but with very low probability.
Read more about this topic: BPP (complexity)
Famous quotes containing the words related and/or classes:
“Women stand related to beautiful nature around us, and the enamoured youth mixes their form with moon and stars, with woods and waters, and the pomp of summer. They heal us of awkwardness by their words and looks. We observe their intellectual influence on the most serious student. They refine and clear his mind: teach him to put a pleasing method into what is dry and difficult.”
—Ralph Waldo Emerson (1803–1882)
“There are four classes of idols which beset men’s minds. To these for distinction’s sake I have assigned names—calling the first class Idols of the Tribe; the second, Idols of the Cave; the third, Idols of the Market-Place; the fourth, Idols of the Theatre.”
—Francis Bacon (1561–1626)