## Abstract

The direct-sum question is a classical question that asks whether performing a task on m independent inputs is m times harder than performing it on a single input. In order to study this question, Beimel et al. [3] introduced the following related problems: • The choice problem: Given m distinct instances, choose one of them and solve it.• The agreement problem: Given m distinct instances, output a solution that is correct for at least one of them.It is easy to see that these problems are no harder than performing the original task on a single instance, and it is natural to ask whether it is strictly easier or not. In particular, proving that the choice problem is not easier is necessary for proving a direct-sum theorem, and is also related to the KRW composition conjecture [12]. In this note, we observe that in a variety of computational models, if f is a random function then with high probability its corresponding choice and agreement problem are not much easier than computing f on a single instance (as long as m is noticeably smaller than 2^{n}).

Original language | English |
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Pages (from-to) | 16-20 |

Number of pages | 5 |

Journal | Information Processing Letters |

Volume | 133 |

DOIs | |

State | Published - May 2018 |

### Bibliographical note

Funding Information:Partially supported by a Motwani Postdoctoral Fellowship and by NSF grant CCF-1749750.

Publisher Copyright:

© 2017 Elsevier B.V.

## Keywords

- Agree
- Choose
- Computational complexity
- Direct sum
- KRW composition conjecture

## ASJC Scopus subject areas

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