Abstract

: Recently, a hierarchy of probabilistic complexity classes generalizing NP has emerged in the work of Babai [B], and Goldwasser, Micali, and Rackoff [GMR1], and Goldwasser and Sipser [GS]. The class IP is defined through the computational model of an interactive prover-verifier pair. Both Turing machines in a pair receive a common input and exchange messages. Every move of the verifier as well as its final determination of whether to accept or reject w are the result of random polynomial time computations on the input and all messages sent so far. The prover has no resource bounds. A language, L, is in IP if there is a prover-verifier pair such that: 1.) when w 2 L, the verifier accepts with probability at least 1 \Gamma 2 \Gammajwj and, 2.) when w 62 L, the verifier interacting with any prover accepts with probability at most 2 \Gammajwj . Such a prover-verifier pair is called an interactive proof for L. In addition to defining interactive proofs, Goldwasser, Micali, and Rackoff...

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