Analysis of Nonlinear Constraints in CLP(R)

Hanus, Michael

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Analysis of Nonlinear Constraints in CLP(R)

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Hanus, Michael
Programming Logics, MPI for Informatics, Max Planck Society;

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Citation

Hanus, M. (1993). Analysis of Nonlinear Constraints in CLP(R). In D. S. Warren (Ed.), Proceedings of the 10th International Conference on Logic Programming (ICLP '93) (pp. 83-99). Cambridge, USA: MIT Press.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-ADDB-2

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.