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:
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.