Efficient probabilistically checkable proofs and applications to approximations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Impossibility results for recycling random bits in two-prover proof systems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
SIAM Journal on Computing
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
Some optimal inapproximability results
Journal of the ACM (JACM)
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Guest column: inapproximability results via Long Code based PCPs
ACM SIGACT News
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
Algebraic methods for interactive proof systems
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Sub-Constant Error Low Degree Test of Almost-Linear Size
SIAM Journal on Computing
Short PCPs with Polylog Query Complexity
SIAM Journal on Computing
Two-query PCP with subconstant error
Journal of the ACM (JACM)
PCP Characterizations of NP: Toward a Polynomially-Small Error-Probability
Computational Complexity
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In a projection PCP, also known as Label-Cover, the verifier makes two queries to the proof, and the answer to the first query determines at most one satisfying answer to the second query. Projection PCPs with low error probability are the basis of most NP-hardness of approximation results known today. In this essay we outline a construction of a projection PCP with low error and low blow-up. This yields sharp approximation thresholds and tight time lower bounds for approximation of a variety of problems, under an assumption on the time required for solving certain NP-hard problems exactly. The approach of the construction is algebraic, and it includes components such as low error, randomness-efficient low degree testing and composition of projection PCPs.