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Continuous If-Then Statements Are Computable

  • Martine CeberioEmail author
  • Vladik Kreinovich
Chapter
  • 1.1k Downloads
Part of the Studies in Computational Intelligence book series (SCI, volume 539)

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  + (x 0) ≠ f (x 0) for some x 0 for which c(x 0) = 0.

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

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References

  1. 1.
    Brattka, V., Gherardi, G.: Weihrauch degrees, omniscience principle, and weak computability. In: Bauer, A., Dillhage, R., Hertling, P., Ko, K.-I., Rettinger, R. (eds.) Proceedings of the Sixth International Conference on Computability and Complexity in Analysis CCA 2009, Ljubljana, Slovenia, August 18-22, pp. 81–92 (2009)Google Scholar
  2. 2.
    Kreinovich, V., Lakeyev, A., Rohn, J., Kahl, P.: Computational Complexity and Feasibility of Data Processing and Interval Computations. Kluwer, Dordrecht (1998)Google Scholar
  3. 3.
    Weihrauch, K.: Computable Analysis: An Introduction. Springer, New York (2000)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of Texas at El PasoEl PasoUSA

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