"Constraint Problems: Computability Is Equivalent to Continuity" by Martine Ceberio and Vladik Kreinovich

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Departmental Technical Reports (CS)

Title

Constraint Problems: Computability Is Equivalent to Continuity

Authors

Martine Ceberio, University of Texas at El PasoFollow
Vladik Kreinovich, University of Texas at El PasoFollow

Publication Date

11-2011

Comments

Technical Report: UTEP-CS-11-56

Abstract

In many practical situations, we would like to compute the set of all possible values that satisfy given constraints. It is known that even for computable (constructive) constraints, computing such set is not always algorithmically possible. One reason for this algorithmic impossibility is that sometimes, the dependence of the desired set on the parameters of the problem is not continuous, while all computable functions of real variables are continuous. In this paper, we show that this discontinuity is the only case when the desired set cannot be computed. Specifically, we provide an algorithm that computes such a set for all the cases when the dependence is continuous.

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