Property testing in bounded degree graphs
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Transforming comparison model lower bounds to the parallel-random-access-machine
Information Processing Letters
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
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
Fast Approximate PCPs for Multidimensional Bin-Packing Problems
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Improved Testing Algorithms for Monotonicity
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Fast approximate probabilistically checkable proofs
Information and Computation
Functions that have read-twice constant width branching programs are not necessarily testable
Random Structures & Algorithms
Tolerant property testing and distance approximation
Journal of Computer and System Sciences
Information theory in property testing and monotonicity testing in higher dimension
Information and Computation
Testing monotonicity over graph products
Random Structures & Algorithms
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
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
Algorithmic Aspects of Property Testing in the Dense Graphs Model
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Approximating the distance to monotonicity in high dimensions
ACM Transactions on Algorithms (TALG)
Monotonicity testing and shortest-path routing on the cube
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Local Monotonicity Reconstruction
SIAM Journal on Computing
Property testing of massively parametrized problems – a survey
Property testing
Transitive-closure spanners: a survey
Property testing
Algorithmic aspects of property testing in the dense graphs model
Property testing
Local property reconstruction and monotonicity
Property testing
Property testing of massively parametrized problems – a survey
Property testing
Transitive-closure spanners: a survey
Property testing
Algorithmic aspects of property testing in the dense graphs model
Property testing
Local property reconstruction and monotonicity
Property testing
Algorithmic Aspects of Property Testing in the Dense Graphs Model
SIAM Journal on Computing
A lower bound for distribution-free monotonicity testing
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
Property testing and the branching program size of boolean functions
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
SIAM Journal on Discrete Mathematics
Optimal bounds for monotonicity and lipschitz testing over hypercubes and hypergrids
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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An ε-test for a property P of functions from D = {1,..., d} to the positive integers is a randomized algorithm, which makes queries on the value of an input function at specified locations, and distinguishes with high probability, between the case of the function satisfying P, and the case that it has to be modified in more than εd places to make it satisfy P. We prove that an ε-test for a property of integer sequences, such as the property of the sequence being a monotone non-decreasing sequence, that depends (in a strict sense) only on the order relations between the sequence members, cannot perform less queries (in the worst case) than the best ε-test which uses only comparisons between the queried values. In addition, we show that an adaptive algorithm for testing that a sequence is monotone non-decreasing performs no better than the best non-adaptive one, with respect to query complexity. From this follows a tight lower bound on tests for this property.