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Communication Complexity of Equality and Error-Correcting Codes

Authors Dale Jacobs , John Jeang , Vladimir Podolskii , Morgan Prior , Ilya Volkovich

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LIPIcs.FSTTCS.2025.37.pdf
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ACM Subject Classification
  • Theory of computation → Communication complexity
  • Theory of computation → Error-correcting codes
  • Theory of computation → Randomness, geometry and discrete structures
Keywords
  • communication complexity
  • randomized communication complexity
  • error-correcting codes

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Abstract

We study the public-coin randomized communication complexity of the equality function. The communication complexity of this function is known to be low when the error probability is constant and the players have access to many random bits. The complexity grows, however, if the allowed error probability and the amount of randomness are restricted.
We show that public-coin randomized protocols for equality and error-correcting codes are essentially the same object. That is, given a protocol for equality, we can construct a code, and vice versa.
We substantially extend the protocol-implies-code direction: any protocol computing a function with a large fooling set can be converted into an error-correcting code. As a corollary, we show that among functions with a fooling set of size s, equality on log s bits has the least randomized communication complexity, regardless of the restrictions on the error probability and the amount of randomness.
Finally, we use the connection to error-correcting codes to analyze the randomized communication complexity of equality for varying restrictions on the error probability and the amount of randomness. In most cases, we provide tight bounds. We pinpoint the setting in which tight bounds are still unknown.

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Dale Jacobs, John Jeang, Vladimir Podolskii, Morgan Prior, and Ilya Volkovich. Communication Complexity of Equality and Error-Correcting Codes. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 37:1-37:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.FSTTCS.2025.37

Author Details

Dale Jacobs
  • Tufts University, Medford, MA, USA
John Jeang
  • Tufts University, Medford, MA, USA
Vladimir Podolskii
  • Tufts University, Medford, MA, USA
Morgan Prior
  • Tufts University, Medford, MA, USA
Ilya Volkovich
  • Boston College, MA, USA

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