License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2020.26
URN: urn:nbn:de:0030-drops-117112
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/11711/
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Chiesa, Alessandro ; Manohar, Peter ; Shinkar, Igor

On Local Testability in the Non-Signaling Setting

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LIPIcs-ITCS-2020-26.pdf (0.7 MB)

Abstract

Non-signaling strategies are a generalization of quantum strategies that have been studied in physics for decades, and have recently found applications in theoretical computer science. These applications motivate the study of local-to-global phenomena for non-signaling functions.
We prove that low-degree testing in the non-signaling setting is possible, assuming that the locality of the non-signaling function exceeds a threshold. We additionally show that if the locality is below the threshold then the test fails spectacularly, in that there exists a non-signaling function which passes the test with probability 1 and yet is maximally far from being low-degree.
Along the way, we present general results about the local testability of linear codes in the non-signaling setting. These include formulating natural definitions that capture the condition that a non-signaling function "belongs" to a given code, and characterizing the sets of local constraints that imply membership in the code. We prove these results by formulating a logical inference system for linear constraints on non-signaling functions that is complete and sound.

BibTeX - Entry

@InProceedings{chiesa_et_al:LIPIcs:2020:11711,
  author =	{Alessandro Chiesa and Peter Manohar and Igor Shinkar},
  title =	{{On Local Testability in the Non-Signaling Setting}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{26:1--26:37},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Thomas Vidick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11711},
  URN =		{urn:nbn:de:0030-drops-117112},
  doi =		{10.4230/LIPIcs.ITCS.2020.26},
  annote =	{Keywords: non-signaling strategies, locally testable codes, low-degree testing, Fourier analysis}
}

Keywords: non-signaling strategies, locally testable codes, low-degree testing, Fourier analysis
Collection: 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)
Issue Date: 2020
Date of publication: 06.01.2020

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