Introduction to finite fields and their applications
Introduction to finite fields and their applications
Checking computations in polylogarithmic time
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
A note on efficient zero-knowledge proofs and arguments (extended abstract)
STOC '92 Proceedings of the twenty-fourth 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
Nearly-linear size holographic proofs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
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)
The random oracle methodology, revisited (preliminary version)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
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
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
A PCP characterization of NP with optimal amortized query complexity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Some optimal inapproximability results
Journal of the ACM (JACM)
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
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
Randomness-efficient low degree tests and short PCPs via epsilon-biased sets
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A Tight Characterization of NP with 3 Query PCPs
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
How to Go Beyond the Black-Box Simulation Barrier
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Computationally efficient error-correcting codes and holographic proofs
Computationally efficient error-correcting codes and holographic proofs
Combinatorics, Probability and 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
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 Complexity of Online Memory Checking
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Sub-constant error low degree test of almost-linear size
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Locally testable codes and PCPs of almost-linear length
Journal of the ACM (JACM)
Combinatorial construction of locally testable codes
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Probabilistic Proof Systems: A Primer
Foundations and Trends® in Theoretical Computer Science
The complexity of online memory checking
Journal of the ACM (JACM)
Probabilistically checkable proofs
Communications of the ACM - Being Human in the Digital Age
Affine dispersers from subspace polynomials
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
Tolerant Linearity Testing and Locally Testable Codes
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Locally testable vs. locally decodable codes
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Locally Testable Codes Require Redundant Testers
SIAM Journal on Computing
Symmetric LDPC codes and local testing
Property testing
Symmetric LDPC codes and local testing
Property testing
Bravely, moderately: a common theme in four recent works
Studies in complexity and cryptography
Limits on the rate of locally testable affine-invariant codes
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Dense locally testable codes cannot have constant rate and distance
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Tolerant locally testable codes
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
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
Robust local testability of tensor products of LDPC codes
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Secure two-party computation with low communication
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
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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We give constructions of probabilistically checkable proofs (PCPs) of length n . poly(log n) (to prove satisfiability of circuits of size n) that can verified by querying poly(log n) bits of the proof. We also give constructions of locally testable codes (LTCs) with similar parameters.Previous constructions of short PCPs (from [5]to [9]) relied extensively on properties of low degree multi-variate polynomials. In contrast, our constructions rely on new problems and techniques revolving around the properties of codes based on high degree polynomials in one variable (also known as Reed-Solomon codes). 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 is simpler than the corresponding steps in previous reductions, and gives a new alternative to using the popular "sum-check protocol". We then give a new PCP for the special task of proving that a function is close to being a Reed-Solomon codeword. This step of the construction is by a self-contained recursion, and the only ingredient needed in the analysis is the bi-variate low-degree test of Polischuk and Spielman[27].Note that our constructions yield LTCs first, which are then converted to PCPs. In contrast, most recent constructions go in the opposite (and less natural) direction of getting LTCs from PCPs.