The Garden Hose Complexity for the Equality Function
Quantum Physics
2013-12-31 v2 Computational Complexity
Abstract
The garden hose complexity is a new communication complexity introduced by H. Buhrman, S. Fehr, C. Schaffner and F. Speelman [BFSS13] to analyze position-based cryptography protocols in the quantum setting. We focus on the garden hose complexity of the equality function, and improve on the bounds of O. Margalit and A. Matsliah[MM12] with the help of a new approach and of our handmade simulated annealing based solver. We have also found beautiful symmetries of the solutions that have lead us to develop the notion of garden hose permutation groups. Then, exploiting this new concept, we get even further, although several interesting open problems remain.
Cite
@article{arxiv.1312.7222,
title = {The Garden Hose Complexity for the Equality Function},
author = {Well Y. Chiu and Mario Szegedy and Chengu Wang and Yixin Xu},
journal= {arXiv preprint arXiv:1312.7222},
year = {2013}
}
Comments
16 pages