Short propositional formulas represent nondeterministic computations
Information Processing Letters
Efficient probabilistically checkable proofs and applications to approximations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Efficient checking of polynomials and proofs and the hardness of approximation problems
Efficient checking of polynomials and proofs and the hardness of approximation problems
Nearly-linear size holographic proofs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Improved low-degree testing and its applications
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)
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
PCP characterizations of NP: towards a polynomially-small error-probability
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Many-Valued Logics and Holographic Proofs
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Clique is hard to approximate within n1-
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Some improvements to total degree tests
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Algebraic methods for interactive proof systems
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Short locally testable codes and proofs: a survey in two parts
Property testing
Short locally testable codes and proofs: a survey in two parts
Property testing
Short locally testable codes and proofs
Studies in complexity and cryptography
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Most known constructions of probabilistically checkable proofs (PCPs) either blow up the proof size by a large polynomial, or have a high (though constant) query complexity. In this paper we give a transformation with slightly-super-cubic blowup in proof size, with a low query complexity. Specifically, the verifier probes the proof in 16 bits and rejects every proof of a false assertion with probability arbitrarily close to 1/2, while accepting corrects proofs of theorems with probability one. The proof is obtained by revisiting known constructions and improving numerous components therein. In the process we abstract a number of new modules that may be of use in other PCP constructions.