## 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(logm)).

Original language | English |
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Pages (from-to) | 105-111 |

Number of pages | 7 |

Journal | Information Processing Letters |

Volume | 136 |

DOIs | |

State | Published - 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