Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Testing subgraphs in large graphs
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
Three theorems regarding testing graph properties
Random Structures & Algorithms
Graph limits and parameter testing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A Characterization of Easily Testable Induced Subgraphs
Combinatorics, Probability and Computing
Testing versus Estimation of Graph Properties
SIAM Journal on Computing
A Characterization of the (Natural) Graph Properties Testable with One-Sided Error
SIAM Journal on Computing
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Hierarchy Theorems for Property Testing
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity
SIAM Journal on Computing
Algorithmic aspects of property testing in the dense graphs model
Property testing
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We consider natural graph property tests, which act entirely independently of the size of the graph being tested. We introduce the notion of properties being inflatable -- closed under taking (balanced) blowups -- and show that the query complexity of natural tests for a property is related to the degree to which it is approximately hereditary and inflatable. Specifically, we show that for properties which are almost hereditary and almost inflatable, any test can be made natural, with a polynomial increase in the number of queries. The naturalization can be considered as an extension of the canonicalization due to [15], so that natural canonical tests can be described as strongly canonical. Using the technique for naturalization, we restore in part the claim in [15] regarding testing hereditary properties by ensuring that a small random subgraph itself satisfies the property. This allows us to generalize the triangle-freeness lower bound result of [5]: Any lower bound, not only the currently established quasi-polynomial one, on one-sided testing for triangle-freeness holds essentially for two-sided testing as well. We also explore the relations of the notion of inflatability and other alreadystudied features of properties and property tests, such as one-sidedness, heredity, and proximity-oblivion.