The original ITIP software (which runs under MATLAB) was developed by Raymond W. Yeung and Ying-On Yan; it is available at http://user-www.ie.cuhk.edu.hk/~ITIP/ The stand-alone version Xitip at http://xitip.epfl.ch has graphical interface, and runs both in Windows and Linux.

This program was written in C, uses the readline library to read entropy expressions; has a user friendly syntax checker; extended syntax; macro facility; online help; glpk (gnu linear programming kit) as the LP solver.

When the command line contains an entropy expression, it is checked for validity (see the section METHOD below). Additional constraints can be specified as additional arguments. Example:

PROMPT> minitip '[a,b,c,d]+(e,b|c)+(e,c|b)+(b,c|e)>=0'
[a,b,c,d]+(e,b|c)+(e,c|b)+(b,c|e)>=0
     ==> FALSE

PROMPT> minitip '[a,b,c,d]+(e,b|c)+(e,c|b)+(b,c|e)>=0' '(e,ad|bc)=0'
[a,b,c,d]+(e,b|c)+(e,c|b)+(b,c|e)>=0
     ==> TRUE with the constraints

The single quotes around the arguments prevent the shell from interpreting special symbols, such as =, <, |, (, and ). Entropy expressions were entered using the simple (or lazy) style: [a,b,c,d] is the Ingleton expression -I(a;b)+I(a;b|c)+I(a;b|d)+I(c;d); letters H and I indicating entropy and mutual information can be omitted; and comma (,) is used as a separator instead of semicolon (;). For full style use the flag -S as follows:

PROMPT> minitip -S '[a;b;c;d]+I(e;b|c)+I(e;c|b)+I(b;c|e)>=-3*I(e;a,d|b,c)'
[a;b;c;d]+I(e;b|c)+I(e;c|b)+I(b;c|e)>=-3*I(e;a,d|b,c)
     ==> TRUE

In interactive usage entropy expressions and constraints are entered at the terminal. Here is an example session.

PROMPT> minitip
minitip: help
 quit        quit minitip
 help        display this text
 ?           synonym for 'help'
 check       check entropy relation with constraints
 test        synonym for 'check'
 xcheck      check entropy relation without constraints
 add         add new constraint
 list        list all or specified constraints: 3,5-7
 del         delete numbered constraint
 unroll      print missing entropy terms on RHS
 ext         convert to extended information measures
 nat         convert to natural coordinates
 macro       add, list, delete macros
 run         execute commands from a file
 style       show / change formula style
 syntax      describe how to enter entropy formulas
 set         list / set runtime parameters
 dump        dump constraints and macro definitions to a file
 save        save command history to a file
 about       history, license, author, etc
 args        accepted command line arguments
minitip: add (e,ad|bc)=0
minitip: list all
Constraints (total 1)
  1: (e,ad|bc)=0
minitip: check [a,b,c,d]+(e,b|c)+(e,c|b)+(b,c|)>=0
----------------------------------------------^
ERROR: variable list is expected here
minitip: check [a,b,c,d]+(e,b|c)+(e,c|b)+(b,c|e)>=0
      ==> TRUE with the constraints
minitip: xcheck [a,b,c,d]+(e,b|c)+(e,c|b)+(b,c|e)>=0
Checking without constraints ...
      ==> FALSE
minitip: quit
Save the commands to the command history file .minitip (y/n)? n
PROMPT> 

Accepted flags and exit values are:

Minitip has several convenience features, such as

run <file>

reads the lines from <file> and executes them as if they were entered from the keyboard. The file can be created by any text editor.

dump <file>

appends all constraints and macros to the given <file>. The file can be edited and then executed to recover the dumped constraints and macros.

save <command-history-file>

saves the commands entered during the session to the given file. The history file is loaded using the command line argument

-f <history-file>

Some features of minitip can be fine-tuned by the 'set' command, such as

• the time and iteration limit on the LP solver;
• how many macros and constraints are accepted;
• whether executing command from a file should stop at all errors, or only at fatal ones;
• whether comment lines (lines starting with a # mark) are printed or not
• command can be abbreviated to any unique prefix
• when finishing, command line history should be automatically saved or not
• in simple style variables ending with digits are accepted or not

When started, minitip looks for the default config file .minitiprc first in the working directory, then in the home directory. If found, the commands are executed before any other action. Alternative config file can be specified by the command line argument

-c <file>

The default config file can be inhibited by using the command line argument '-c-'. A sample config file can be

# sample .minitiprc
# comment lines in run files are printed
set comment=yes
# forget history when quitting minitip
set save=no
# allow abbreviated commands
set abbrev=yes
# don't stop run files for non-fatal errors
set run=loose
# define a macro
macro D(a,b,c)=(a,b|c)+(a,c|b)+(b,c|a)
# print all commands
help
# that's all ...

After collecting all random variables in the expression (and constraints), the program creates all Shannon entropy inequalities for those variables. Then checks whether the expression is a consequence of the constraints and the Shannon inequalities. It is done by creating a Linear Program instance, and calling an LP solver. Thus the result printed out by the program is the answer to the following question:

Does this inequality follow from the (basic) Shannon inequalities, and from the given constraints?

and not whether the given inequality is a valid entropy inequality (that is, holds for arbitrary collection of random variables).

The size of the LP problem can be very big. Using 10 random variables there will be 1023 entropies (one for all nonempty subsets), and over 11500 Shannon inequalities. The Shannon inequalities form a numerically ill-conditioned (highly degenerate) LP instance, thus, from time to time, any LP solver will give erroneous answer. Please watch for those cases.

The original ITIP software was created and written by Raymond W. Yeung and Ying-On Yan; it is available at http://user-www.ie.cuhk.edu.hk/~ITIP. It runs under MATLAB. The stand-alone version Xitip at http://xitip.epfl.ch has graphical interface and runs both in Windows and Linux. This version is written in C from scratch, and has extended syntax, more user friendly syntax checker, and uses the glpk LP solver.

The program uses the 'readline' library and include files, and the 'glpk' library and include files. The following line should compile it on linux without any problem:

 gcc -O3 *.c -lglpk -lreadline -o minitip

Laszlo Csirmaz, csirmaz@ceu.edu