# Arthur–Merlin protocol

## Interactive proof system in computational complexity theory / From Wikipedia, the free encyclopedia

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In computational complexity theory, an **Arthur–Merlin protocol**, introduced by Babai (1985), is an interactive proof system in which the verifier's coin tosses are constrained to be public (i.e. known to the prover too). Goldwasser & Sipser (1986) proved that all (formal) languages with interactive proofs of arbitrary length with private coins also have interactive proofs with public coins.

Given two participants in the protocol called Arthur and Merlin respectively, the basic assumption is that Arthur is a standard computer (or verifier) equipped with a random number generating device, while Merlin is effectively an oracle with infinite computational power (also known as a prover). However, Merlin is not necessarily honest, so Arthur must analyze the information provided by Merlin in response to Arthur's queries and decide the problem itself. A problem is considered to be solvable by this protocol if whenever the answer is "yes", Merlin has some series of responses which will cause Arthur to accept at least 2⁄3 of the time, and if whenever the answer is "no", Arthur will never accept more than 1⁄3 of the time. Thus, Arthur acts as a probabilistic polynomial-time verifier, assuming it is allotted polynomial time to make its decisions and queries.