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Communication Complexity with Defective Randomness

Authors Marshall Ball, Oded Goldreich, Tal Malkin

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Author Details

Marshall Ball
  • Computer Science Department, Columbia University, New York, NY, USA
Oded Goldreich
  • Faculty of Mathematics and Computer Science, Weizmann Institute of Science, Rehovot, Israel
Tal Malkin
  • Computer Science Department, Columbia University, New York, NY, USA

Funding

This work was supported in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA) via Contract No. 2019-1902070006. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either express or implied, of ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein.
  • Ball, Marshall: Partially supported by an IBM Research PhD Fellowship.
  • Goldreich, Oded: Partially supported by an ISF grant number (Nr. 1146/18); research was conducted while he enjoyed the hospitality of the computer science department at Columbia University.

Cite As Get BibTex

Marshall Ball, Oded Goldreich, and Tal Malkin. Communication Complexity with Defective Randomness. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 14:1-14:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.CCC.2021.14

Abstract

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Communication complexity
Keywords
  • Randomized Communication Complexity
  • Randomness Extraction
  • Min-Entropy

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References

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