The main technical contribution is a construction of a “length-efficient” robust PCP of proximity, which does differ from previous constructions in fundamental ways, and in particular does not use the “parallelization” step of Arora et al.Expand

A direct-sum theorem in communication complexity is derived by employing a rejection sampling procedure that relates the relative entropy between two distributions to the communication complexity of generating one distribution from the other.Expand

The techniques include the introduction of a new variant of PCPs that are called "Robust PCPs", which facilitate proof composition, which is a central ingredient in construction of PCP systems.Expand

It is shown that low treewidth is indeed the only structural restriction of the underlying graph that can ensure tractability, and that even for the "best case" graph structure, there is no inference algorithm with complexity polynomial in thetreewidth.Expand

It is proved that there are 3CNF properties that require a linear number of queries, even for adaptive tests, which contrasts with 2C NF properties that are testable with O(√n) queries.Expand

We show that every language in NP has a probabilistically checkable proof of proximity (i.e., proofs asserting that an instance is "close" to a member of the language), where the verifier's running… Expand

A generic composition theorem for low-error two-query probabilistically checkable proofs (PCPs) is presented, which generalizes and abstracts the work of Moshkovitz and Raz and constructed almost linear-sized low- error 2-query PCPs for every language in NP.Expand

A modular and simpler proof of the main result of this paper is a generic composition theorem for low error two-query probabilistically checkable proofs (PCPs), which works regardless of the way the component PCPs are constructed.Expand

Using the first deterministic quasi-polynomial time algorithms for approximately counting the number of solutions to a broad class of integer programs, including dense covering problems and contingency tables, the invariance principle is given.Expand