ACM Transactions on Computation Theory (TOCT)
Short PCPPs verifiable in polylogarithmic time with O(1) queries
Annals of Mathematics and Artificial Intelligence
Two-query PCP with subconstant error
Journal of the ACM (JACM)
Low rate is insufficient for local testability
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Guest column: testing linear properties: some general theme
ACM SIGACT News
Short locally testable codes and proofs: a survey in two parts
Property testing
Composition of low-error 2-query PCPs using decodable PCPs
Property testing
Short locally testable codes and proofs: a survey in two parts
Property testing
Composition of low-error 2-query PCPs using decodable PCPs
Property testing
Short locally testable codes and proofs
Studies in complexity and cryptography
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
On the rectangle method in proofs of robustness of tensor products
Information Processing Letters
The tensor product of two good codes is not necessarily robustly testable
Information Processing Letters
Guest column: algebraic construction of projection PCPs
ACM SIGACT News
SIAM Journal on Discrete Mathematics
Taking proof-based verified computation a few steps closer to practicality
Security'12 Proceedings of the 21st USENIX conference on Security symposium
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Resolving the conflict between generality and plausibility in verified computation
Proceedings of the 8th ACM European Conference on Computer Systems
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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We give constructions of probabilistically checkable proofs (PCPs) of length $n \cdot polylog n$ proving satisfiability of circuits of size $n$ that can be verified by querying $polylog n$ bits of the proof. We also give analogous constructions of locally testable codes (LTCs) mapping $n$ information bits to $n\cdot polylog n$ bit long codewords that are testable with $polylog n$ queries. Our constructions rely on new techniques revolving around properties of codes based on relatively high-degree polynomials in one variable, i.e., Reed-Solomon codes. In contrast, previous constructions of short PCPs, beginning with [L. Babai, L. Fortnow, L. Levin, and M. Szegedy, Checking computations in polylogarithmic time, in Proceedings of the 23rd ACM Symposium on Theory of Computing, ACM, New York, 1991, pp. 21-31] and until the recent [E. Ben-Sasson, O. Goldreich, P. Harsha, M. Sudan, and S. Vadhan, Robust PCPs of proximity, shorter PCPs, and applications to coding, in Proceedings of the 36th ACM Symposium on Theory of Computing, ACM, New York, 2004, pp. 13-15], relied extensively on properties of low-degree polynomials in many variables. We show how to convert the problem of verifying the satisfaction of a circuit by a given assignment to the task of verifying that a given function is close to being a Reed-Solomon codeword, i.e., a univariate polynomial of specified degree. This reduction also gives an alternative to using the “sumcheck protocol” [C. Lund, L. Fortnow, H. Karloff, and N. Nisan, J. ACM, 39 (1992), pp. 859-868]. We then give a new PCP for the special task of proving that a function is close to being a Reed-Solomon codeword. The resulting PCPs are not only shorter than previous ones but also arguably simpler. In fact, our constructions are also more natural in that they yield locally testable codes first, which are then converted to PCPs. In contrast, most recent constructions go in the opposite direction of getting locally testable codes from PCPs.