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Simplification procedures

For a specific problem the end-user may have some knowledge of the
problem that implies that he may determine that for some intervals
for the variables the problem has no solution, that the intervals
for some variables may be reduced or that a solution may be found.
Most of the ALIAS C++ solving programs have an optional argument that
allows then end-user to provide this knowledge as a procedure, that
will be called a *simplification procedure*.

Usually this procedure will take as input a set of intervals for the
variables and will return an integer which is typically:

- -1 if there is no solution to the problem at hand for the given
set of intervals
- 1 if the routine has allowed to reduce the width of the
intervals of the set
- 0 if the routine has not changed the set of intervals
- if the procedure has provided a solution to the problem

As these simplification procedures are very important for solving
efficiently most problems we will devote the specific
chapter 4 for those
used in system solving. More specific simplification procedures will
be presented together with the solving algorithms.

** Next:** General purpose system solving
** Up:** Introduction
** Previous:** Storage mode
** Contents**
Jean-Pierre Merlet
2012-12-20