Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Computability
Complexity theory of real functions
Complexity theory of real functions
A Theory of Program Size Formally Identical to Information Theory
Journal of the ACM (JACM)
Computable analysis: an introduction
Computable analysis: an introduction
Weakly computable real numbers
Journal of Complexity
A characterization of c.e. random reals
Theoretical Computer Science
A Finite Hierarchy of the Recursively Enumerable Real Numbers
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Recursively Enumerable Reals and Chaitin Omega Numbers
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Binary enumerability of real numbers
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
On the hierarchy and extension of monotonically computable real numbers
Journal of Complexity
| Hi-index | 5.23 |
In effective analysis, various classes of real numbers are discussed. For example, the classes of computable, semi-computable, weakly computable, recursively approximable real numbers, etc. All these classes correspond to some kind of (weak) computability of the real numbers. In this paper we discuss mathematical closure properties of these classes under the limit, effective limit and computable function. Among others, we show that the class of weakly computable real numbers is not closed under effective limit and partial computable functions while the class of recursively approximable real numbers is closed under effective limit and partial computable functions.