"Is It Possible to Have a Feasible Enclosure-Computing Method Which Is " by Marcin Michalak and Vladik Kreinovich

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Departmental Technical Reports (CS)

Title

Is It Possible to Have a Feasible Enclosure-Computing Method Which Is Independent of the Equivalent Form?

Authors

Marcin Michalak, Silesian University of Technology
Vladik Kreinovich, University of Texas at El PasoFollow

Publication Date

6-2011

Comments

Technical Report: UTEP-CS-11-35

Abstract

The problem of computing the range [y] of a given function f(x1, ..., xn) over given intervals [xi] -- often called the main problem of interval computations -- is, in general, NP-hard. This means that unless P = NP, it is not possible to have a feasible (= polynomial time) algorithm that always computes the desired range. Instead, interval computations algorithms compute an enclosure [Y] for the desired range. For all known feasible enclosure-computing methods -- starting with straightforward interval computations -- there exist two expressions f(x1, ..., xn) and g(x1, ..., xn) for computing the same function that lead to different enclosures. We prove that, unless P = NP, this is inevitable: it is not possible to have a feasible enclosure-computing method which is independent of the equivalent form.

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