Improved Monotone Circuit Depth Upper Bound for Directed Graph Reachability
Computational Complexity
2008-09-23 v1
Abstract
We prove that the directed graph reachability problem (transitive closure) can be solved by monotone fan-in 2 boolean circuits of depth (1/2+o(1))(log n)^2, where n is the number of nodes. This improves the previous known upper bound (1+o(1))(log n)^2. The proof is non-constructive, but we give a constructive proof of the upper bound (7/8+o(1))(log n)^2.
Keywords
Cite
@article{arxiv.0809.3614,
title = {Improved Monotone Circuit Depth Upper Bound for Directed Graph Reachability},
author = {Sergey Volkov},
journal= {arXiv preprint arXiv:0809.3614},
year = {2008}
}
Comments
preprint