In complexity theory
(Zero-error Probabilistic Polynomial time) is the set of problems for which a probabilistic Turing machine
exists with these properties:
- It always returns the correct YES or NO answer
- The running time is random, but on average is polynomial
In other words, the algorithm is allowed to flip a truly-random coin while it's running. It always returns the correct answer. For a problem of size n
, there is some polynomial p
) such that the average running time will be less than p
), even though it might occasionally be much longer.
The class ZPP is exactly equal to the intersection of the classes RP and Co-RP.
The definition of ZPP is based on probabilistic Turing machines. Other complexity classes based on them include BPP and RP. The class BQP is based on another machine with randomness: the quantum computer.