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On rank vs. communication complexity

Abstract

This paper concerns the open problem of Lovász and Saks regarding the relationship between the communication complexity of a boolean function and the rank of the associated matrix. We first give an example exhibiting the largest gap known. We then prove two related theorems.

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A preliminary version of this paper appeared in [10].

This work was supported by USA-Israel BSF grant 92-00043 and by a Wolfeson research award administered by the Israeli Academy of Sciences.

This work was supported by USA-Israel BSF grant 92-00106 and by a Wolfeson research award administered by the Israeli Academy of Sciences.

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Nisan, N., Wigderson, A. On rank vs. communication complexity. Combinatorica 15, 557–565 (1995). https://doi.org/10.1007/BF01192527

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Mathematics Subject Classification (1991)

  • 68Q05
  • 68R05
  • 05C50