Checking computations in polylogarithmic time
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Efficient probabilistically checkable proofs and applications to approximations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
Nearly-linear size holographic proofs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Probabilistic checking of proofs and hardness of approximation problems
Probabilistic checking of proofs and hardness of approximation problems
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
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)
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
A Combinatorial Consistency Lemma with Application to Proving the PCP Theorem
SIAM Journal on Computing
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Locally Testable Codes and PCPs of Almost-Linear Length
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Some 3CNF properties are hard to test
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Randomness-efficient low degree tests and short PCPs via epsilon-biased sets
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Some improvements to total degree tests
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Robust pcps of proximity, shorter pcps and applications to coding
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Assignment Testers: Towards a Combinatorial Proof of the PCP-Theorem
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
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
Linearity testing in characteristic two
IEEE Transactions on Information Theory - Part 1
List decoding tensor products and interleaved codes
Proceedings of the forty-first annual ACM symposium on Theory of computing
Guest column: testing linear properties: some general theme
ACM SIGACT News
Limitation on the rate of families of locally testable codes
Property testing
Limitation on the rate of families of locally testable codes
Property testing
Efficient probabilistically checkable debates
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
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
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We continue the investigation of locally testable codes, i.e., error-correcting codes for which membership of a given word in the code can be tested probabilistically by examining it in very few locations. We give two general results on local testability: First, motivated by the recently proposed notion of robust probabilistically checkable proofs, we introduce the notion of robust local testability of codes. We relate this notion to a product of codes introduced by Tanner and show a very simple composition lemma for this notion. Next, we show that codes built by tensor products can be tested robustly and somewhat locally by applying a variant of a test and proof technique introduced by Raz and Safra in the context of testing low-degree multivariate polynomials (which are a special case of tensor codes). Combining these two results gives us a generic construction of codes of inverse polynomial rate that are testable with poly-logarithmically many queries. We note that these locally testable tensor codes can be obtained from any linear error correcting code with good distance. Previous results on local testability, albeit much stronger quantitatively, rely heavily on algebraic properties of the underlying codes. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006Research supported in part by a Radcliffe Fellowship.Research supported in part by a Radcliffe Fellowship and by NSF Award CCR-0219218.