License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CCC.2021.14
URN: urn:nbn:de:0030-drops-142886
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Ball, Marshall ; Goldreich, Oded ; Malkin, Tal

Communication Complexity with Defective Randomness

LIPIcs-CCC-2021-14.pdf (0.6 MB)


Starting with the two standard model of randomized communication complexity, we study the communication complexity of functions when the protocol has access to a defective source of randomness. Specifically, we consider both the public-randomness and private-randomness cases, while replacing the commonly postulated perfect randomness with distributions over 𝓁 bit strings that have min-entropy at least k ≤ 𝓁. We present general upper and lower bounds on the communication complexity in these cases, where the bounds are typically linear in 𝓁-k and also depend on the size of the fooling set for the function being computed and on its standard randomized complexity.

BibTeX - Entry

  author =	{Ball, Marshall and Goldreich, Oded and Malkin, Tal},
  title =	{{Communication Complexity with Defective Randomness}},
  booktitle =	{36th Computational Complexity Conference (CCC 2021)},
  pages =	{14:1--14:10},
  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 =		{},
  URN =		{urn:nbn:de:0030-drops-142886},
  doi =		{10.4230/LIPIcs.CCC.2021.14},
  annote =	{Keywords: Randomized Communication Complexity, Randomness Extraction, Min-Entropy}

Keywords: Randomized Communication Complexity, Randomness Extraction, Min-Entropy
Collection: 36th Computational Complexity Conference (CCC 2021)
Issue Date: 2021
Date of publication: 08.07.2021

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