We show that the computational problem CONSENSUS-HALVING is PPA-complete, the first PPA-completeness result for a problem whose definition does not involve an explicit circuit. We also show that an approximate version of this problem is polynomial-time equivalent to NECKLACE SPLITTING, which establishes PPAD-hardness for NECKLACE SPLITTING, and suggests that it is also PPA-complete.
@article{arxiv.1711.04503,
title = {Consensus Halving is PPA-Complete},
author = {Aris Filos-Ratsikas and Paul W. Goldberg},
journal= {arXiv preprint arXiv:1711.04503},
year = {2017}
}