README

This repository contains files that describe the inequalities that govern certain causal
structures. These structures are described in the Master Thesis by Laurens Ligthart.

The repository is split up into maps that contain files for different causal structures.
The causal structures that have been discussed are:

Extended triangle
Extended triangle with connections
Causal #9
Causal #11
General cccq
General ccqq

There are three file types:

.ine 			The H-representation for the lrs programs
.ext			The V-representation for the lrs programs
.ieq			The H-representation for the Porta programs

For information about formating of .ine or .ext files, we refer to the documentation for
lrslib at http://cgm.cs.mcgill.ca/~avis/C/lrs.html. For information about formatting of
.ieq files, we refer to the Porta documentation at http://comopt.ifi.uni-heidelberg.de/software/PORTA/

All files are based on Shannon and von Neumann inequalities and (in)equalities implied 
by the causal structure. In addition, other inequalities were included based on the file 
name:

noZY			-
class			Classical Zhang-Yeung (ZY) inequalities
quantum			cccq and ccqq ZY inequalities
ZY				Classical, cccq and ccqq ZY inequalities
allZY			All classical and quantum ZY inequalities (including unproven ones)
allqZY			All quantum ZY inequalities (including unproven ones)
families_x		Classical, cccq and ccqq ZY inequalities, and inequalities of the 
				infinite family up to s=x for ccqc ZY inequalities

If the filename contains the letters FM, the Fourier-Motzkin elimination was successful.
The file then contains the relevant inequalities for the 2^4-1=15 remaining entries of 
the entropy vector if it is an .ine or .ieq file, or the extremal rays of the 15 dimen-
sional cone if it is an .ext file. Otherwise, the file contains the relevant inequalities 
that hold before the Fourier-Motzkin elimination is performed.
Redundancy has been removed from all .ine files with the redund program of lrs.

For questions, feel free to send an email to laurensligthart@gmail.com