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Abstract

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.