A separation theorem in property testing

13 years 4 months ago

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Consider the following seemingly rhetorical question: Is it crucial for a property-tester to know the error parameter in advance? Previous papers dealing with various testing problems, suggest that the answer may be no, as in these papers there was no loss of generality in assuming that is given as part of the input, and is not known in advance. Our main result in this paper, however, is that it is possible to separate a natural model of property testing in which is given as part of the input from the model in which is known in advance (without making any computational hardness assumptions). To this end, we construct a graph property P, which has the following two properties: (i) There is no tester for P accepting as part of the input, whose number of queries depends only on . (ii) For any fixed , there is a tester for P (that works only for that specific ), which makes a constant number of queries. Interestingly, we manage to construct a separating property P, which is combinatoriall...

Noga Alon, Asaf Shapira

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