## Analysis of Nonlinear Constraints in {CLP($\cal{R}$)}

**Michael Hanus**
*Technical Report MPI-I-92-251, Max-Planck-Institut fuer Informatik*

*Short version in Proc. 10th International Conference on
Logic Programming (ICLP '93)*

Solving nonlinear constraints over real numbers is a complex problem.
Hence constraint logic programming languages like
CLP($\cal R$) or Prolog III solve only linear constraints
and delay nonlinear constraints until they become linear.
This efficient implementation method has the disadvantage
that sometimes computed answers are unsatisfiable or infinite
loops occur due to the unsatisfiability of delayed nonlinear
constraints. These problems could be solved by using a more
powerful constraint solver which can deal with nonlinear
constraints like in RISC-CLP(Real). Since such powerful
constraint solvers are not very efficient, we propose a
compromise between these two extremes. We characterize a
class of CLP($\cal R$) programs for which all delayed nonlinear
constraints become linear at run time. Programs belonging
to this class can be safely executed with the efficient
CLP($\cal R$) method while the remaining programs need a
more powerful constraint solver.

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