Direct Sums for Parity Decision Trees
Computational Complexity
2025-06-03 v2
Abstract
Direct sum theorems state that the cost of solving instances of a problem is at least times the cost of solving a single instance. We prove the first such results in the randomised parity decision tree model. We show that a direct sum theorem holds whenever (1) the lower bound for parity decision trees is proved using the discrepancy method; or (2) the lower bound is proved relative to a product distribution.
Cite
@article{arxiv.2412.06552,
title = {Direct Sums for Parity Decision Trees},
author = {Tyler Besselman and Mika Göös and Siyao Guo and Gilbert Maystre and Weiqiang Yuan},
journal= {arXiv preprint arXiv:2412.06552},
year = {2025}
}
Comments
39 pages