Efficient proof verification is at the heart of the study of computation. Seminal results such as the IP=PSPACE Theorem [LFKN92,Shamir92] and the PCP theorem [AS92,ALMSS92] show that even highly complicated statements can be verified extremely efficiently.
We study the complexity of proving statements using interactive protocols. Specifically, what statements can be proved by a polynomial-time prover to a super-efficient verifier. Our main results show that these proof-system are remarkably powerful: it is possible to prove the correctness of general computations such that (1) the prover runs in polynomial-time, (2) the verifier runs in linear-time (and in some conditions in sublinear-time) and (3) the interaction consists of only a constant number of communication rounds (and in some settings just a single round).
These proof-systems are motivated by, and have applications for, delegating computations in a cloud computing environment, and guaranteeing that they were performed correctly.
Ron Rothblum, CSAIL, MIT.