Definition: The class of languages for which membership can be determined in polynomial time by a probabilistic Turing machine with no false acceptances and less than half false rejections. "RP" means "Randomized Polynomial" time.

Formal Definition: For a language, S, there exists a probabilistic Turing machine, M, that accepts or rejects any string in polynomial time. If w ∉ S, M rejects w. If w ∈ S, M accepts w with a probability at least 1/2.

Also known as randomized polynomial time.

See also NP, ZPP, BPP, Monte Carlo algorithm.

Note: By repeating the run, the chance of incorrect rejection may be arbitrarily reduced.

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, "RP", in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 17 December 2004. (accessed TODAY) Available from: