Complexity theory of real functions
Complexity theory of real functions
Computable analysis: an introduction
Computable analysis: an introduction
Characterization of the Computable Real Numbers by Means of Primitive Recursive Functions
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
On the representations of NC and log-space real numbers
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
On logarithmic-space computable real numbers
Theoretical Computer Science
| Hi-index | 0.00 |
In mathematics, various representations of real numbers have been investigated. All these representations are mathematically equivalent because they lead to the same real structure-Dedekind-complete ordered field. Even the effective versions of these representations are equivalent in the sense that they define the same notion of computability of real numbers. However, the primitive recursive (p.r., for short) versions of these representations can lead to different notions of p.r. real numbers. Several interesting results about p.r. real numbers can be found in literatures. In this paper we summarize the known results about the primitive recursiveness of real numbers for different representations as well as show some new relationships. Our goal is to clarify systematically how the primitive recursiveness depends on the representations of the real numbers.