Characterization theorem for the conditionally computable real functions
The class of uniformly computable real functions with respect to a small subrecursive class of operators computes the elementary functions of calculus, restricted to compact subsets of their domains. The class of conditionally computable real functions with respect to the same class of operators is...
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| Format: | Article |
| Language: | English |
| Published: |
Logical Methods in Computer Science e.V.
2017-07-01
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| Series: | Logical Methods in Computer Science |
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| Online Access: | https://lmcs.episciences.org/3772/pdf |
| Summary: | The class of uniformly computable real functions with respect to a small
subrecursive class of operators computes the elementary functions of calculus,
restricted to compact subsets of their domains. The class of conditionally
computable real functions with respect to the same class of operators is a
proper extension of the class of uniformly computable real functions and it
computes the elementary functions of calculus on their whole domains. The
definition of both classes relies on certain transformations of infinitistic
names of real numbers. In the present paper, the conditional computability of
real functions is characterized in the spirit of Tent and Ziegler, avoiding the
use of infinitistic names. |
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| ISSN: | 1860-5974 |