Fully parallelized multi prover protocols for NEXP-time

A major open problem in the theory of multiprover protocols is to characterize the languages which can be accepted by fully parallelized protocols which achieve an exponentially low probability of cheating in a single round. The problem was motivated by the observation that the probability of cheating the n parallel executions of a multiprover protocol can be exponentially higher than the probability of cheating in n sequential executions of the same protocol. The problem is solved by proving that any language in NEXP-time has a fully parallelized multiprover protocol. By combining this result with a fully parallelized version of the protocol of M. Ben-Or et al. (ACM Symp. on Theory of Computing, 1988), a one-round perfect zero-knowledge protocol (under no cryptographic assumptions) can be obtained for every NEXPTIME language.<>