Improved low-degree testing and its applications
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A black box approach to the algebraic set decomposition problem
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)
Small PCPs with Low Query Complexity
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects 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
Algebraic testing and weight distributions of codes
Theoretical Computer Science
Almost Orthogonal Linear Codes are Locally Testable
FOCS '05 Proceedings of the 46th 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
Robust locally testable codes and products of codes
Random Structures & Algorithms
Locally testable codes and PCPs of almost-linear length
Journal of the ACM (JACM)
Low-end uniform hardness vs. randomness tradeoffs for AM
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
The complexity of online memory checking
Journal of the ACM (JACM)
Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
Short locally testable codes and proofs: a survey in two parts
Property testing
Invariance in property testing
Property testing
Short locally testable codes and proofs: a survey in two parts
Property testing
Invariance in property testing
Property testing
Short locally testable codes and proofs
Studies in complexity and cryptography
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
New affine-invariant codes from lifting
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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
| Hi-index | 0.00 |
Abstract: A low-degree test is a collection of simple, local rules for checking the proximity of an arbitrary function to a low-degree polynomial. Each rule depends on the function's values at a small number of places. If a function satisfies many rules then it is close to a low-degree polynomial. Low-degree tests play an important role in the development of probabilistically checkable proofs. In this paper we present two improvements to the efficiency of low-degree tests. Our first improvement concerns the smallest field size over which a low-degree test can work. We show how to test that a function is a degree d polynomial over prime fields of size only d+2. Our second improvement shows a better efficiency of the low-degree test of Rubinfeld and Sudan (1993) than previously known. We show concrete applications of this improvement via the notion of "locally checkable codes". This improvement translates into better tradeoffs on the size versus probe complexity of probabilistically checkable proofs than previously known.