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Property testing and sublinear algorithms for languages and combinatorial properties (Property Testing)
Start date: Jul 1, 2008, End date: Jun 30, 2013 PROJECT  FINISHED 

Property testing, an investigation started in [Blum, Luby and Rubinfeld, 1993], [Rubinfeld and Sudan, 1996], and [Goldreich, Goldwasser and Ron, 1996], deals with the following general question: Distinguish, using as few queries as possible, between the case where the input satisfies a certain property, and the case where the input is epsilon-far from this, i.e. the case where there is no way to make the input satisfy the given property even if it is modified in an epsilon fraction of its positions. Ideally the number of queries, i.e. the size of the portion of the input that is read by the (probabilistic) algorithm, depends only on epsilon and does not depend at all on the input length. However, algorithms that read more than a constant amount, as long as it is sublinear in the input size, are also deemed interesting. The related topic of sublinear algorithms concentrate on similar notions of approximation, but with the stronger requirement that the running time (rather than query complexity) that is less than the order of the input size. The purpose of this proposal is to investigate advanced topics in the frontier of property testing, especially with respect to the relation of the easiness of testing to other notions of complexity, and to investigate possible uses of ideas from property testing in other fields of computer science. Particular emphasis will be given to hypergraph-like models, sparse models, and models in which the description of the property in itself is represented as a graph or a combinatorial structure. The latter holds particular promise with regards to applications both inside and outside theoretical CS. Some topics going beyond testing (such as stronger testing notions, and testing-related notions from Probabilistically Checkable Proofs) will also be addressed.

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