Recycling queries in PCPs and in linearity tests

Abstract

Query-efficient Probabilistically Checkable Proofs (PCPs) and linearity tests are studied, focusing on the number of amortized query bits. A testing algorithm uses q̄ bits and has error probability at most 2-k. The best known PCP construction for NP in this respect uses 3 amortized query bits; at least one amortized query bit necessary, unless P = NP. The best known linearity test uses 3 amortized query bits; a different one achieves 1 amortized free bit but uses an unbounded number of amortized query bits.