Definition: The class of languages for which a membership computation by a probabilistic Turing machine halts in polynomial time with no false acceptances or rejections, but randomly some "I don't know" answers. "ZPP" means "Zero error Probability in Polynomial" time.

Formal Definition: For a language, S, there exists a probabilistic Turing machine, M, that halts in polynomial time. M (correctly) accepts or rejects the string or, randomly, halts in an "I don't know" state.

See also RP, NP, BPP, Las Vegas algorithm.

Note: By repeating the run, the correct answer will always be found, albeit with polynomial expected run time.

After [Hirv01, page 19].

Author: PEB

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Entry modified 17 December 2004.
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Cite this as:
Paul E. Black, "ZPP", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 17 December 2004. (accessed TODAY) Available from: