Finitely Bounded Effective Computability

Authors:
Xizhong Zheng
Affiliations:
Department of Computer Science, Jiangsu University, Zhenjiang 212013, P.R. China and Theoretische Informatik, BTU Cottbus, D-03044 Cottbus, Germany
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2008

Citing 3
Cited 0

Weakly computable real numbers

Journal of Complexity
A hierarchy of Turing degrees of divergence bounded computable real numbers

Journal of Complexity
Classification of the Computable Approximations by Divergence Boundings

Electronic Notes in Theoretical Computer Science (ENTCS)

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Abstract

One of the most important property of the computability is the certainty. For example a set of natural numbers is computable if there is a Turing machine which decides certainly if a given natural number belongs to the set or not, and no wrong answers are tolerant. On the other hand, the finitely bounded computability discussed in this paper allows finitely many mistakes which can be eventually corrected during an effective procedure. We will show especially that the class of finitely bounded computable real numbers has very interesting properties, and it is a real closed field containing even properly in the class of d-c.e. real numbers.