The algorithmic aspects of the regularity lemma
Journal of Algorithms
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Constructive Quasi-Ramsey Numbers and Tournament Ranking
SIAM Journal on Discrete Mathematics
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
The regularity lemma and approximation schemes for dense problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Extremal Graph Theory
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Some 3CNF properties are hard to test
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Functions that have read-once branching programs of quadratic size are not necessarily testable
Information Processing Letters
Functions that have read-twice constant width branching programs are not necessarily testable
Random Structures & Algorithms
The difficulty of testing for isomorphism against a graph that is given in advance
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Every monotone graph property is testable
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Testing versus estimation of graph properties
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Testing hypergraph colorability
Theoretical Computer Science - Automata, languages and programming
A large lower bound on the query complexity of a simple boolean function
Information Processing Letters
A Characterization of the (natural) Graph Properties Testable with One-Sided Error
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
A large lower bound on the query complexity of a simple boolean function
Information Processing Letters
Property testing and parameter testing for permutations
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Testing permutation properties through subpermutations
Theoretical Computer Science
A note on the testability of ramsey's class
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
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Let P be a property of graphs. An ∈-test for P is a randomized algorithm which, given the ability to make queries whether a desired pair of vertices of an input graph G with n vertices are adjacent or not, distinguishes, with high probability, between the case of G satisfying P and the case that it has to be modified by adding and removing more than ∈(n 2) edges to make it satisfy P. The property P is called testable, if for every ∈ there exists an ∈-test for P whose total number of queries is independent of the size of the input graph. Goldreich, Goldwasser and Ron [7] showed that certain graph properties, like k-colorability, admit an ∈-test. In [2] a first step towards a logical characterization of the testable graph properties was made by proving that all first order properties of type “∃∀” are testable while there exist first order graph properties of type “∀∃” which are not testable. For proving the positive part, it was shown that all properties describable by a very general type of coloring problem are testable.While this result is tight from the standpoint of first order expressions, further steps towards the characterization of the testable graph properties can be taken by considering the coloring problem instead. It is proven here that other classes of graph properties, describable by various generalizations of the coloring notion used in [2], are testable, showing that this approach can broaden the understanding of the nature of the testable graph properties. The proof combines some generalizations of the methods used in [2] with additional methods.