Multi-prover encoding schemes and three-prover proof systems

Suppose two provers agree in a polynomial p and want to reveal a single value y=p(x) to a verifier where m is chosen arbitrarily by the verifier. Whereas honest provers should be able to agree on any polynomial p the verifier wants to be sure that with any (cheating) pair of provers the value y he receives is a polynomial function of x. We formalize this question and introduce multi-prover (quasi-)encoding schemes to solve it. Multi-prover quasi-encoding schemes are used to develop new interactive proof techniques. The main result of M. Bellare et al. (1993) is the existence of one-round four-prover interactive proof system for any language an NP achieving any constant error probability with O(log n) random bits and poly(log log n) answer-sizes. We improve this result in two respects. First we decrease the number of provers to three, and then we decrease the answer-size to a constant. Reduction of each parameter de critical for applications. When the error-probability is required to approach zero, our technique is efficient in the number of random bits and in the answer size.<>