Continuous If-Then Statements Are Computable

Authors

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

Publication Date

9-2009

Comments

Technical Report: UTEP-CS-09-28

Published in: Martine Ceberio (ed.), Abstracts of the Second Workshop on Constraint Programming and Decision Making CoProD'09, El Paso, Texas, November 9-10, 2009, pp. 11-14.

Abstract

In many practical situations, we must compute the value of an if-then expression f(x) defined as "if c(x) >= 0 then f₊(x) else f_-(x)", where f₊(x), f_-(x), and c(x) are computable functions. The value f(x) cannot be computed directly, since in general, it is not possible to check whether a given real number c(x) is non-negative or non-positive. Similarly, it is not possible to compute the value f(x) if the if-then function is discontinuous, i.e., when f₊(x₀) =/= f_-(x₀) for some x₀ for which c(x₀) = 0.

In this paper, we show that if the if-then expression is continuous, then we can effectively compute f(x).