Computational Complexity
Computational complexity theory models randomized algorithms as probabilistic Turing machines. Both Las Vegas and Monte Carlo algorithms are considered, and several complexity classes are studied. The most basic randomized complexity class is RP, which is the class of decision problems for which there is an efficient (polynomial time) randomized algorithm (or probabilistic Turing machine) which recognizes NO-instances with absolute certainty and recognizes YES-instances with a probability of at least 1/2. The complement class for RP is co-RP. Problem classes having (possibly nonterminating) algorithms with polynomial time average case running time whose output is always correct are said to be in ZPP.
The class of problems for which both YES and NO-instances are allowed to be identified with some error is called BPP. This class acts as the randomized equivalent of P, i.e. BPP represents the class of efficient randomized algorithms.
Read more about this topic: Randomized Algorithm
Famous quotes containing the word complexity:
“The price we pay for the complexity of life is too high. When you think of all the effort you have to put in—telephonic, technological and relational—to alter even the slightest bit of behaviour in this strange world we call social life, you are left pining for the straightforwardness of primitive peoples and their physical work.”
—Jean Baudrillard (b. 1929)