## 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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