Real recursive functions and real extensions of recursive functions

Olivier Bournez; Emmanuel Hainry

doi:10.1007/978-3-540-31834-7_9

Real recursive functions and real extensions of recursive functions

Olivier Bournez
, Emmanuel Hainry

LORIA Laboratoire Lorrain de Recherche en Informatique et ses Applications

Research output: Contribution to journal › Conference article › peer-review

Abstract

Recently, functions over the reals that extend elementarily computable functions over the integers have been proved to correspond to the smallest class of real functions containing some basic functions and closed by composition and linear integration. We extend this result to all computable functions: functions over the reals that extend total recursive functions over the integers are proved to correspond to the smallest class of real functions containing some basic functions and closed by composition, linear integration and a very natural unique minimization schema.

Original language	English
Pages (from-to)	116-127
Number of pages	12
Journal	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3354
DOIs	https://doi.org/10.1007/978-3-540-31834-7_9
Publication status	Published - 1 Jan 2005
Externally published	Yes
Event	4th International Conference on Machines, Computations, and Universality, MCU 2004 - Saint Petersburg, Russian Federation Duration: 21 Sept 2004 → 24 Sept 2004

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10.1007/978-3-540-31834-7_9

Cite this

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AB - Recently, functions over the reals that extend elementarily computable functions over the integers have been proved to correspond to the smallest class of real functions containing some basic functions and closed by composition and linear integration. We extend this result to all computable functions: functions over the reals that extend total recursive functions over the integers are proved to correspond to the smallest class of real functions containing some basic functions and closed by composition, linear integration and a very natural unique minimization schema.

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JO - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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ER -

Real recursive functions and real extensions of recursive functions

Abstract

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