Fischer, E. and Lachish, Oded and Vasudev, Y. (2015) Trading query complexity for sample-based testing and multi-testing scalability. Symposium on Foundations of Computer Science , pp. 1163-1182. ISSN 0272-5428.
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Abstract
We show that every non-adaptive property testing algorithm making a constant number of queries, over a fixed alphabet, can be converted to a sample-based (as per [Goldreich and Ron, 2015]) testing algorithm whose average number of queries is a fixed, smaller than $1$, power of $n$. Since the query distribution of the sample-based algorithm is not dependent at all on the property, or the original algorithm, this has many implications in scenarios where there are many properties that need to be tested for concurrently, such as testing (relatively large) unions of properties, or converting a Merlin-Arthur Proximity proof (as per [Gur and Rothblum, 2013]) to a proper testing algorithm. The proof method involves preparing the original testing algorithm for a combinatorial analysis. For the analysis we develop a structural lemma for hypergraphs that may be of independent interest. When analyzing a hypergraph that was extracted from a $2$-sided test, it allows for finding generalized sunflowers that provide for a large-deviation type analysis. For $1$-sided tests the bounds can be improved further by applying Janson's inequality directly over our structures.
Metadata
| Item Type: | Article |
|---|---|
| Additional Information: | IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS), 17 Oct - 20 Oct 2015, Berkeley, CA, USA. (c) 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. |
| School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
| Depositing User: | Dr Oded Lachish |
| Date Deposited: | 11 Feb 2016 12:50 |
| Last Modified: | 09 Aug 2023 12:37 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/13240 |
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