Abstract
In property testing, the goal is to distinguish between objects that satisfy some desirable property and objects that are far from satisfying it, after examining only a small, random sample of the object in question. Although much of the literature has focused on properties of graphs, very recently several strong results on hypergraphs have appeared. We revisit a logical result obtained by Alon et al. [1] in the light of these recent results. The main result is the testability of all properties (of relational structures) expressible in sentences of Ramsey’s class.
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References
Alon, N., Fischer, E., Krivelevich, M., Szegedy, M.: Efficient testing of large graphs. Combinatorica 20(4), 451–476 (2000)
Alon, N., Shapira, A.: A characterization of the (natural) graph properties testable with one-sided error. SIAM J. Comput. 37(6), 1703–1727 (2008)
Alon, N., Shapira, A.: A separation theorem in property testing. Combinatorica 28(3), 261–281 (2008)
Austin, T., Tao, T.: On the testability and repair of hereditary hypergraph properties. arXiv.org as arXiv:0801.2179v2 (2009) (preprint)
Börger, E., Grädel, E., Gurevich, Y.: The Classical Decision Problem. Springer, Heidelberg (1997)
Enderton, H.B.: A Mathematical Introduction to Logic, 2nd edn. Academic Press, London (2000)
Fischer, E.: Testing graphs for colorability properties. In: Proceedings, 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 873–882 (2001)
Fischer, E.: Testing graphs for colorability properties. Random Struct. Algorithms 26(3), 289–309 (2005)
Jordan, C., Zeugmann, T.: Relational properties expressible with one universal quantifier are testable. In: Watanabe, O., Zeugmann, T. (eds.) SAGA 2009. LNCS, vol. 5792, pp. 141–155. Springer, Heidelberg (2009)
Kolaitis, P., Vardi, M.: The decision problem for the probabilities of higher-order properties. In: STOC 1987: Proceedings of the 19th Annual ACM Symposium on Theory of Computing, pp. 425–435. ACM, New York (1987)
Lewis, H.R.: Complexity results for classes of quantificational formulas. J. Comput. Syst. Sci. 21(3), 317–353 (1980)
Ramsey, F.P.: On a problem of formal logic. Proc. London Math. Soc. 30(2), 264–286 (1930)
Rödl, V., Schacht, M.: Property testing in hypergraphs and the removal lemma. In: STOC 2007: Proceedings of the 39th Annual ACM Symposium on Theory of Computing, pp. 488–495. ACM, New York (2007)
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Jordan, C., Zeugmann, T. (2010). A Note on the Testability of Ramsey’s Class. In: Kratochvíl, J., Li, A., Fiala, J., Kolman, P. (eds) Theory and Applications of Models of Computation. TAMC 2010. Lecture Notes in Computer Science, vol 6108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13562-0_27
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DOI: https://doi.org/10.1007/978-3-642-13562-0_27
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