2 Search Results for "Baleshzar, Roksana"


Document
Lower Bounds for Tolerant Junta and Unateness Testing via Rejection Sampling of Graphs

Authors: Amit Levi and Erik Waingarten

Published in: LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)


Abstract
We introduce a new model for testing graph properties which we call the rejection sampling model. We show that testing bipartiteness of n-nodes graphs using rejection sampling queries requires complexity Omega~(n^2). Via reductions from the rejection sampling model, we give three new lower bounds for tolerant testing of Boolean functions of the form f : {0,1}^n -> {0,1}: - Tolerant k-junta testing with non-adaptive queries requires Omega~(k^2) queries. - Tolerant unateness testing requires Omega~(n) queries. - Tolerant unateness testing with non-adaptive queries requires Omega~(n^{3/2}) queries. Given the O~(k^{3/2})-query non-adaptive junta tester of Blais [Eric Blais, 2008], we conclude that non-adaptive tolerant junta testing requires more queries than non-tolerant junta testing. In addition, given the O~(n^{3/4})-query unateness tester of Chen, Waingarten, and Xie [Xi Chen et al., 2017] and the O~(n)-query non-adaptive unateness tester of Baleshzar, Chakrabarty, Pallavoor, Raskhodnikova, and Seshadhri [Roksana Baleshzar et al., 2017], we conclude that tolerant unateness testing requires more queries than non-tolerant unateness testing, in both adaptive and non-adaptive settings. These lower bounds provide the first separation between tolerant and non-tolerant testing for a natural property of Boolean functions.

Cite as

Amit Levi and Erik Waingarten. Lower Bounds for Tolerant Junta and Unateness Testing via Rejection Sampling of Graphs. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 52:1-52:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{levi_et_al:LIPIcs.ITCS.2019.52,
  author =	{Levi, Amit and Waingarten, Erik},
  title =	{{Lower Bounds for Tolerant Junta and Unateness Testing via Rejection Sampling of Graphs}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{52:1--52:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{124},
  editor =	{Blum, Avrim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.52},
  URN =		{urn:nbn:de:0030-drops-101452},
  doi =		{10.4230/LIPIcs.ITCS.2019.52},
  annote =	{Keywords: Property Testing, Juntas, Tolerant Testing, Boolean functions}
}
Document
Optimal Unateness Testers for Real-Valued Functions: Adaptivity Helps

Authors: Roksana Baleshzar, Deeparnab Chakrabarty, Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, and C. Seshadhri

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)


Abstract
We study the problem of testing unateness of functions f:{0,1}^d -> R. We give an O(d/\epsilon . log(d/\epsilon))-query nonadaptive tester and an O(d/\epsilon)-query adaptive tester and show that both testers are optimal for a fixed distance parameter \epsilon. Previously known unateness testers worked only for Boolean functions, and their query complexity had worse dependence on the dimension both for the adaptive and the nonadaptive case. Moreover, no lower bounds for testing unateness were known. We generalize our results to obtain optimal unateness testers for functions f:[n]^d -> R. Our results establish that adaptivity helps with testing unateness of real-valued functions on domains of the form {0,1}^d and, more generally, [n]^d. This stands in contrast to the situation for monotonicity testing where there is no adaptivity gap for functions f:[n]^d -> R.

Cite as

Roksana Baleshzar, Deeparnab Chakrabarty, Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, and C. Seshadhri. Optimal Unateness Testers for Real-Valued Functions: Adaptivity Helps. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


Copy BibTex To Clipboard

@InProceedings{baleshzar_et_al:LIPIcs.ICALP.2017.5,
  author =	{Baleshzar, Roksana and Chakrabarty, Deeparnab and Pallavoor, Ramesh Krishnan S. and Raskhodnikova, Sofya and Seshadhri, C.},
  title =	{{Optimal Unateness Testers for Real-Valued Functions: Adaptivity Helps}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{5:1--5:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.5},
  URN =		{urn:nbn:de:0030-drops-74844},
  doi =		{10.4230/LIPIcs.ICALP.2017.5},
  annote =	{Keywords: Property testing, unate and monotone functions}
}
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