Two Query PCP with Sub-Constant Error

We show that the NP-Complete language 3SAT has a PCP verifier that makes two queries to a proof of almost-linear size and achieves sub-constant probability of error o(1). The verifier performs only projection tests, meaning that the answer to the first query determines at most one accepting answer to the second query. Previously, by the parallel repetition theorem, there were PCP Theorems with two-query projection tests, but only (arbitrarily small) constant error and polynomial size [29]. There were also PCP Theorems with sub-constant error and almost-linear size, but a constant number of queries that is larger than 2 [26]. As a corollary, we obtain a host of new results. In particular, our theorem improves many of the hardness of approximation results that are proved using the parallel repetition theorem. A partial list includes the following:

• Type: Conference
• Year: 2008
• Where: FOCS
• Authors: Dana Moshkovitz, Ran Raz
• Keywords: FOCS 2008, Parallel Repetition Theorem, PCP Theorems, Projection Tests, Theoretical Computer Science