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.

Complexity-theoretic properties

It is known that BPP is

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