(definition)

**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 "**Z**ero error **P**robability in **P**olynomial" 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: https://www.nist.gov/dads/HTML/zpp.html