Adler, I orcid.org/0000-0002-9667-9841, Köhler, N and Peng, P (2021) GSF-Locality Is Not Sufficient For Proximity-Oblivious Testing. In: Kabanets, V, (ed.) Proceedings of 36th Computational Complexity Conference (CCC 2021). 36th Computational Complexity Conference (CCC 2021), 20-23 Jul 2021, Toronto, Canada. Leibniz International Proceedings in Informatics (LIPIcs), 200 . Schloss Dagstuhl - Leibniz-Zentrum für Informatik , 34:1-34:27. ISBN 978-3-95977-193-1
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 |
---|---|
Authors/Creators: |
|
Editors: |
|
Copyright, Publisher and Additional Information: | © Isolde Adler, Noleen Köhler, and Pan Peng. This is an open access conference paper under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | Property testing, proximity-oblivous testing, locality, first-order logic, lower bound |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 18 Jun 2021 13:25 |
Last Modified: | 07 Aug 2023 14:43 |
Status: | Published |
Publisher: | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Series Name: | Leibniz International Proceedings in Informatics (LIPIcs) |
Identification Number: | 10.4230/LIPIcs.CCC.2021.34 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:175354 |