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URN: urn:nbn:de:0030-drops-143082
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GSF-Locality Is Not Sufficient For Proximity-Oblivious Testing

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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.

BibTeX - Entry

@InProceedings{adler_et_al:LIPIcs.CCC.2021.34,
  author =	{Adler, Isolde and K\"{o}hler, Noleen and Peng, Pan},
  title =	{{GSF-Locality Is Not Sufficient For Proximity-Oblivious Testing}},
  booktitle =	{36th Computational Complexity Conference (CCC 2021)},
  pages =	{34:1--34:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-193-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{200},
  editor =	{Kabanets, Valentine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14308},
  URN =		{urn:nbn:de:0030-drops-143082},
  doi =		{10.4230/LIPIcs.CCC.2021.34},
  annote =	{Keywords: Property testing, proximity-oblivous testing, locality, first-order logic, lower bound}
}

Keywords: Property testing, proximity-oblivous testing, locality, first-order logic, lower bound
Seminar: 36th Computational Complexity Conference (CCC 2021)
Issue date: 2021
Date of publication: 08.07.2021


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