Under the auspices of the Computational Complexity Foundation (CCF)

REPORTS > KEYWORD > MONOTONE COMPLEXITY:
Reports tagged with monotone complexity:
TR02-007 | 14th January 2002
Pavel Pudlak

#### Monotone complexity and the rank of matrices

The rank of a matrix has been used a number of times to prove lower
bounds on various types of complexity. In particular it has been used
for the size of monotone formulas and monotone span programs. In most
cases that this approach was used, there is not a single ... more >>>

TR12-185 | 29th December 2012
Siu Man Chan, Aaron Potechin

#### Tight Bounds for Monotone Switching Networks via Fourier Analysis

We prove tight size bounds on monotone switching networks for the NP-complete problem of
$k$-clique, and for an explicit monotone problem by analyzing a pyramid structure of height $h$ for
the P-complete problem of generation. This gives alternative proofs of the separations of m-NC
from m-P and of m-NC$^i$ from ... more >>>

TR15-171 | 28th October 2015
Joshua Grochow

#### Monotone projection lower bounds from extended formulation lower bounds

In this short note, we show that the permanent is not complete for non-negative polynomials in $VNP_{\mathbb{R}}$ under monotone p-projections. In particular, we show that Hamilton Cycle polynomial and the cut polynomials are not monotone p-projections of the permanent. To prove this we introduce a new connection between monotone projections ... more >>>

TR16-013 | 12th January 2016
Ludwig Staiger

#### Bounds on the Kolmogorov complexity function for infinite words

Revisions: 1

The Kolmogorov complexity function of an infinite word $\xi$ maps a natural
number to the complexity $K(\xi|n)$ of the $n$-length prefix of $\xi$. We
investigate the maximally achievable complexity function if $\xi$ is taken
from a constructively describable set of infinite words. Here we are
interested ... more >>>

TR16-139 | 8th September 2016
Ludwig Staiger

#### Exact constructive and computable dimensions

Revisions: 1

In this paper we derive several results which generalise the constructive
dimension of (sets of) infinite strings to the case of exact dimension. We