Bounds on monotone switching networks for directed connectivity

TL;DR

This paper establishes a lower bound on the size of monotone switching networks for directed connectivity, demonstrating a fundamental complexity separation in monotone computational models.

Contribution

It proves that any monotone switching network solving directed connectivity requires superpolynomial size, separating monotone analogues of L and NL.

Findings

Monotone switching networks for directed connectivity have size at least n^{Omega(log n)}.

This result separates monotone versions of L and NL complexity classes.

The lower bound highlights inherent complexity in monotone network models.

Abstract

We separate monotone analogues of L and NL by proving that any monotone switching network solving directed connectivity on $n$ vertices must have size at least $n^(\Omega(\lg(n)))$.