Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
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)
Locally Testable Codes and PCPs of Almost-Linear Length
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Randomness-efficient low degree tests and short PCPs via epsilon-biased sets
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Robust pcps of proximity, shorter pcps and applications to coding
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Simple PCPs with poly-log rate and query complexity
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Short PCPs Verifiable in Polylogarithmic Time
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Some 3CNF Properties Are Hard to Test
SIAM Journal on Computing
The PCP theorem by gap amplification
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The tensor product of two codes is not necessarily robustly testable
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Combinatorial construction of locally testable codes
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Tensor Products of Weakly Smooth Codes Are Robust
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
List decoding tensor products and interleaved codes
Proceedings of the forty-first annual ACM symposium on Theory of computing
Composition of Semi-LTCs by Two-Wise Tensor Products
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Guest column: testing linear properties: some general theme
ACM SIGACT News
List Decoding Tensor Products and Interleaved Codes
SIAM Journal on Computing
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
A new family of locally correctable codes based on degree-lifted algebraic geometry codes
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Given two binary linear codes R and C, their tensor product R⊗C consists of all matrices with rows in R and columns in C. We analyze the “robustness” of the following test for this code (suggested by Ben-Sasson and Sudan [6]): Pick a random row (or column) and check if the received word is in R (or C). Robustness of the test implies that if a matrix M is far from R⊗C, then a significant fraction of the rows (or columns) of M are far from codewords of R (or C). We show that this test is robust, provided one of the codes is what we refer to as smooth. We show that expander codes and locally-testable codes are smooth. This complements recent examples of P. Valiant [13] and Coppersmith and Rudra [9] of codes whose tensor product is not robustly testable.