A separation theorem in property testing

A separation theorem in property testing

Consider the following seemingly rhetorical question: Is it crucial for a property-tester to know the error parameter 2 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 2 is given as part of the input, and is not known in advance. Our main result in this paper, however, is th...

An Adaptivity Hierarchy Theorem for Property Testing

Adaptivity is known to play a crucial role in property testing. In particular, there exist properties for which there is an exponential gap between the power of adaptive testing algorithms, wherein each query may be determined by the answers received to prior queries, and their nonadaptive counterparts, in which all queries are independent of answers obtained from previous queries. In this work...

A nonconvex separation property in Banach spaces

We establish, in innnite dimensional Banach space, a nonconvex separation property for general closed sets that is an extension of Hahn-Banach separation theorem. We provide some consequences in optimization, in particular the existence of singular multipliers and show the relation of our principle with the extremal principle of Mordukhovich.

Invariance in Property Testing

Property testing considers the task of testing rapidly (in particular, with very few samples into the data), if some massive data satisfies some given property, or is far from satisfying the property. For “global properties”, i.e., properties that really depend somewhat on every piece of the data, one could ask how it can be tested by so few samples? We suggest that for “natural” properties, th...

Property Testing