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Definitions for and reductions among NC approximation problems
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Definitions and reductions for NC approximation problems

Definitions and reductions for NC approximation problems

This file was last updated on 25 October 2012.


This paper can be found at

To download the paper using Git, run

git clone git://

A somewhat recent version of this work should be available at, but I can't guarantee that that will always be up to date, since I compile and upload it manually.

Compilation dependencies

Besides pdflatex, compile-time dependencies include the following LaTeX packages:

  • amsmath
  • amssymb
  • amsthm
  • complexity
  • hyperref
  • tikz

On Ubuntu 11.04, 11.10, 12.04, or 12.10, the necessary system packages which contain these LaTeX packages are:

  • texlive-base
  • texlive-latex-base
  • texlive-pictures
  • texlive-science

To install them, run

sudo apt-get install texlive-base texlive-latex-base texlive-pictures \


To compile the document, run

pdflatex ncapproximation
bibtex ncapproximation
pdflatex ncapproximation
pdflatex ncapproximation

The output is ncapproximation.pdf, and can be viewed with any PDF reader.


Copyright 2012 Jeffrey Finkelstein.

Except where otherwise noted, both the LaTeX markup and the content of both the article and the poster are made available under the terms of the Creative Commons Attribution-ShareAlike 3.0 license,


Jeffrey Finkelstein

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