Many hard examples for resolution
Journal of the ACM (JACM)
Randomized algorithms
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Testing graphs for colorable properties
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Monotonicity testing over general poset domains
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Regular Languages are Testable with a Constant Number of Queries
SIAM Journal on Computing
Testing Membership in Languages that Have Small Width Branching Programs
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
A Lower Bound for Testing 3-Colorability in Bounded-Degree Graphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Functions that have Read-Twice Constant Width Branching Programs are not Necessarily Testable
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Computationally efficient error-correcting codes and holographic proofs
Computationally efficient error-correcting codes and holographic proofs
Functions that have read-twice constant width branching programs are not necessarily testable
Random Structures & Algorithms
Robust pcps of proximity, shorter pcps and applications to coding
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A large lower bound on the query complexity of a simple boolean function
Information Processing Letters
Almost Orthogonal Linear Codes are Locally Testable
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A combinatorial characterization of the testable graph properties: it's all about regularity
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Robust locally testable codes and products of codes
Random Structures & Algorithms
Algebraic property testing: the role of invariance
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On the Benefits of Adaptivity in Property Testing of Dense Graphs
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
A large lower bound on the query complexity of a simple boolean function
Information Processing Letters
Short locally testable codes and proofs: a survey in two parts
Property testing
Short locally testable codes and proofs: a survey in two parts
Property testing
Short locally testable codes and proofs
Studies in complexity and cryptography
Property testing and the branching program size of boolean functions
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Space complexity vs. query complexity
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
Calibrating noise to sensitivity in private data analysis
TCC'06 Proceedings of the Third conference on Theory of Cryptography
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For a boolean formula φ on n variables, the associated property Pφ is the collection of n-bit strings that satisfy φ. We prove that there are 3CNF properties that require a linear number of queries, even for adaptive tests. This contrasts with 2CNF properties that are testable with O(√n) queries[7]. Notice that for every bad instance (i.e. an assignment that does not satisfy φ) there is a 3-bit query that witnesses this fact. Nevertheless, finding such a short witness requires a linear number of queries, even for assignments that are very far from satisfying.We provide sufficient conditions for linear properties to be hard to test, and in the course of the proof include a couple of observations which are of independent interest.