| N. Alon, S. Ben-David, N. Ceqa-Bianchi, D. Haussler, Scale-sensitive dimensions, unitbrm cinvergence, and learnability, Proc. 341h Annual Symp. on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1993, pp. 292-301. |
....implicitly proven already in [13] for k = 2 and in [27] see also [2] for general k, using the Regularity Lemma of Szemeredi [30] but in the context of property testing it is first studied in [21] where far more e#cient algorithms are described. These have been further improved in [7] In [5] it is shown that every first order graph property without a quantifier alternation of type ## has # testers whose query complexity is independent of the size of the input graph (but has a huge dependence on #) In [1] it is shown that there is a one sided error # tester for checking H freeness ....
....[30] adapted for directed graphs, which we formulate and prove. This version of the regularity lemma might prove useful for other problems. The application for getting the strong testability of each property PH is similar to the proof for the undirected case, given (implicitly) in [2] see also [5], 1] The one sided # tester for PH for arbitrary digraphs H, has query complexly bounded by a function which, though independent of the size of the input digraph G, has a huge dependency on # and the size of H. For some digraphs H, however, there are more e#cient # testers; for example, if H is ....
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N. Alon, E. Fischer, M. Krivelevich and M. Szegedy, E#cient testing of large graphs, Proc. 40 Annual Symp. on Foundations of Computer Science (FOCS), New York, NY, IEEE (
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N. Alon, S. Ben-David, N. Ceqa-Bianchi, D. Haussler, Scale-sensitive dimensions, unitbrm cinvergence, and learnability, Proc. 341h Annual Symp. on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1993, pp. 292-301.
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