Journal of the ACM (JACM)
Random Debaters and the Hardness of Approximating Stochastic Functions
SIAM Journal on Computing
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Word problems requiring exponential time(Preliminary Report)
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Beyond NP: the work and legacy of Larry Stockmeyer
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Robust locally testable codes and products of codes
Random Structures & Algorithms
The PCP theorem by gap amplification
Journal of the ACM (JACM)
Robust PCPs of Proximity, Shorter PCPs, and Applications to Coding
SIAM Journal on Computing
Assignment Testers: Towards a Combinatorial Proof of the PCP Theorem
SIAM Journal on Computing
SFCS '76 Proceedings of the 17th Annual Symposium on Foundations of Computer Science
Algebraic methods for interactive proof systems
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Nondeterministic exponential time has two-prover interactive protocols
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Infeasibility of instance compression and succinct PCPs for NP
Journal of Computer and System Sciences
Towards coding for maximum errors in interactive communication
Proceedings of the forty-third annual ACM symposium on Theory of computing
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Linear-time encodable and decodable error-correcting codes
IEEE Transactions on Information Theory - Part 1
Coding for interactive communication
IEEE Transactions on Information Theory - Part 1
Hi-index | 0.00 |
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 natural PSPACE-complete problems are also PSPACE-complete. We give an improved construction of these debates: for any language L that has an ordinary debate system definable by uniform circuits of size s = s(n), we give a PCDS for L whose debate is of total bitlength: Õ(s), with a verifier that uses only log2 s+log2(polylog(s)) bits of randomness. This yields a much tighter connection between the time complexity of natural PSPACE-complete problems and the time complexity of their approximation versions. Our key ingredient is a novel application of error-resilient communication protocols, as developed by Schulman; we use the more recent protocol of Braverman and Rao. We show that by requiring ordinary debates to be encoded in an error-resilient fashion, we can endow them with a useful "stability" property. Stable debates can then be transformed into PCDSs, by applying efficient PCPPs (as given by Dinur). Our main technical challenge in building stable debates is to enforce error-resilient encoding by the debaters. To achieve this, we show that there is a constant-round debate system, with a very efficient verifier, to debate whether a communication transcript follows the Braverman-Rao protocol.