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\input zb-ioport
\iteman{io-port 05117083}
\itemau{Bournez, Olivier; Hainry, Emmanuel}
\itemti{Recursive analysis characterized as a class of real recursive functions.}
\itemso{Fundam. Inform. 74, No. 4, 409-433 (2006).}
\itemab
Summary: Recently, using a limit schema, we presented an analog and machine-independent algebraic characterization of elementary functions over the real numbers in the sense of recursive analysis. In a different and orthogonal work, we proposed a minimalization schema that provides a class of real recursive functions that corresponds to extensions of computable functions over the integers. Mixing the two approaches we prove that computable functions over the real numbers in the sense of recursive analysis can be characterized as the smallest class of functions that contains some basic functions, and closed by composition, linear integration, minimalization and limit schema.
\itemrv{~}
\itemcc{}
\itemut{recursive analysis; real recursive functions; computable functions over the reals}
\itemli{}
\end