Improving exhaustive search implies superpolynomial lower bounds
Proceedings of the forty-second ACM symposium on Theory of computing
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
Combinatorial algorithms for distributed graph coloring
DISC'11 Proceedings of the 25th international conference on Distributed computing
On efficient zero-knowledge PCPs
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Delegation of computation with verification outsourcing: curious verifiers
Proceedings of the 2013 ACM symposium on Principles of distributed computing
On the concrete efficiency of probabilistically-checkable proofs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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The PCP theorem asserts the existence of proofs that can be verified by a verifier that reads only a very small part of the proof. The theorem was originally proved by Arora and Safra (J. ACM 45(1)) and Arora et al. (J. ACM 45(3)) using sophisticated algebraic tools. More than a decade later, Dinur (J. ACM 54(3)) gave a simpler and arguably more intuitive proof using alternative combinatorial techniques. One disadvantage of Dinur's proof compared to the previous algebraic proof is that it yields less efficient verifiers. In this work, we provide a combinatorial construction of PCPs with verifiers that are as efficient as the ones obtained by the algebraic methods. The result is the first combinatorial proof of the PCP theorem for (originally proved by Babai et al., STOC 1991), and a combinatorial construction of super-fast PCPs of Proximity for (first constructed by Ben-Sasson et al., CCC 2005).