One-sided Vs Two-sided Error
Whereas the answer returned by a deterministic algorithm is always expected to be correct, this is not the case for Monte Carlo algorithms. For decision problems, these algorithms are generally classified as either false-biased or true-biased. A false-biased Monte Carlo algorithm is always correct when it returns false; a true-biased algorithm is always correct when it returns true. While this describes algorithms with one-sided errors, others might have no bias; these are said to have two-sided errors. The answer they provide (either true or false) will be incorrect, or correct, with some bounded probability.
For instance, the Solovay–Strassen primality test is used to determine whether a given number is a prime number. It always answers true for prime number inputs; for composite inputs, it answers false with probability at least 1/2 and true with probability at most 1/2. Thus, false answers from the algorithm are certain to be correct, whereas the true answers remain uncertain; this is said to be a (1/2)-correct false-biased algorithm.
Read more about this topic: Monte Carlo Algorithm
Famous quotes containing the word error:
“Never miss an opportunity to allow a child to do something she can and wants to on her own. Sometimes were in too much of a rushand she might spill something, or do it wrong. But whenever possible she needs to learn, error by error, lesson by lesson, to do better. And the more she is able to learn by herself the more she gets the message that shes a kid who can.”
—Polly Berrien Berends (20th century)