Sub-Constant Error Probabilistically Checkable Proof of Almost-Linear Size

A Note on Almost Perfect Probabilistically Checkable Proofs of Proximity

Probabilistically checkable proofs of proximity (PCPP) are proof systems where the verifier is given a 3SAT formula, but has only oracle access to an assignment and a proof. The verifier accepts a satisfying assignment with a valid proof, and rejects (with high enough probability) an assignment that is far from all satisfying assignments (for any given proof). In this work, we focus on the type...

Probabilistically Checkable Proofs

Probabilistically Checkable Proofs

Efficient Probabilistically Checkable Debates

Probabilistically checkable debate systems (PCDSs) are debates between two competing provers, in which a polynomial-time verifier inspects a constant number of bits of the debate. It was shown by Condon, Feigenbaum, Lund, and Shor that every language in PSPACE has a PCDS in which the debate length is polynomially bounded. Using this result, they showed that the approximation versions of some na...

Restricted probabilistically checkable proofs

In this work we provide some initial structural complexity results for classes of probabilistically checkable proof systems (PCPs) for nondeterministic NC (NNC) circuit families, as a first step towards characterizing probabilistic proof systems for P. One of the major successes of the characterization of NP as a class of PCPs (with polynomial time verifiers) is that it provides a route to prov...