Linear Projection in Clp(fd) | Draft

The problem of quantiier elimination, or projection, is to reduce the dimensions of a constraint to the desired ones without changing the solution set. Such a method is best known for linear dense domains. Systems like ECL i PS e and CLP(R) provide a projection module to eliminate the dead variables of the linear part of answers. But elimination can be more than a lter of the answer. It can also be used as an instrument for reducing the size of a problem. We have successfully applied early projection to linear real planning problems. We have shown that their performance depends heavily on a projection before the end of computation. When applied to integer nite domain (FD) constraints, the real-valued elimination methods return a complete but not necessarily correct answer. If the integers are relatively big, the errors may be acceptable. Some restricted cases are treated correctly. We apply Fourier to a ow-shop scheduling system, the solution of which is substantially simpliied. Since propagation in FD is not complete, redundant constraints may help to increase it. Projection gives a semi-automatic method for obtaining redundant constraints from a set of linear FD constraints.