The direct sum of universal relations

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Abstract

The universal relation is the communication problem in which Alice and Bob get as inputs two distinct strings, and they are required to find a coordinate on which the strings differ. The study of this problem is motivated by its connection to Karchmer–Wigderson relations [12], which are communication problems that are tightly related to circuit-depth lower bounds. In this paper, we prove a direct sum theorem for the universal relation, namely, we prove that solving m independent instances of the universal relation is m times harder than solving a single instance. More specifically, it is known that the deterministic communication complexity of the universal relation is at least n. We prove that the deterministic communication complexity of solving m independent instances of the universal relation is at least m⋅(n−O(log⁡m)).

Original languageEnglish
Pages (from-to)105-111
Number of pages7
JournalInformation Processing Letters
Volume136
DOIs
StatePublished - Aug 2018

Bibliographical note

Funding Information:
Partially supported by the Israel Science Foundation (grant No. 1445/16). Part of this research was done while Or Meir was supported by Irit Dinur's ERC grant number 239986.

Publisher Copyright:
© 2018 Elsevier B.V.

Keywords

  • Communication complexity
  • Computational complexity
  • Direct sum
  • Karchmer–Wigderson relations
  • Universal relation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications

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