Adler, I., Köhler, N. and Peng, P. orcid.org/0000-0003-2700-5699 (2021) GSF-locality is not sufficient for proximity-oblivious testing. In: Kabanets, V., (ed.) 36th Computational Complexity Conference (CCC 2021). Computational Complexity Conference (CCC), 20-22 Jul 2021, Virtual conference (Toronto, Ontario, Cananda). Leibniz International Proceedings in Informatics (LIPIcs), 200 . Schloss Dagstuhl - Leibniz-Zentrum für Informatik , 34:1-34:27. ISBN 9783959771931
Abstract
In Property Testing, proximity-oblivious testers (POTs) form a class of particularly simple testing algorithms, where a basic test is performed a number of times that may depend on the proximity parameter, but the basic test itself is independent of the proximity parameter. In their seminal work, Goldreich and Ron [STOC 2009; SICOMP 2011] show that the graph properties that allow constant-query proximity-oblivious testing in the bounded-degree model are precisely the properties that can be expressed as a generalised subgraph freeness (GSF) property that satisfies the non-propagation condition. It is left open whether the non-propagation condition is necessary. Indeed, calling properties expressible as a generalised subgraph freeness property GSF-local properties, they ask whether all GSF-local properties are non-propagating. We give a negative answer by exhibiting a property of graphs that is GSF-local and propagating. Hence in particular, our property does not admit a POT, despite being GSF-local. We prove our result by exploiting a recent work of the authors which constructed a first-order (FO) property that is not testable [SODA 2021], and a new connection between FO properties and GSF-local properties via neighbourhood profiles.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © Isolde Adler, Noleen Köhler, and Pan Peng; licensed under Creative Commons License CC-BY 4.0. https://creativecommons.org/licenses/by/4.0/legalcode |
Keywords: | Property testing; proximity-oblivous testing; locality; first-order logic; lower bound |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 09 Jun 2021 07:29 |
Last Modified: | 28 Sep 2021 15:51 |
Status: | Published |
Publisher: | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Series Name: | Leibniz International Proceedings in Informatics (LIPIcs) |
Refereed: | Yes |
Identification Number: | 10.4230/LIPIcs.CCC.2021.34 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:174661 |