Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Complexity theory of real functions
Complexity theory of real functions
Topological complexity with continuous operations
Journal of Complexity - Special issue for the Foundations of Computational Mathematics conference, Rio de Janeiro, Brazil, Jan. 1997
Computable analysis: an introduction
Computable analysis: an introduction
Complexity theory on real numbers and functions
Proceedings of the 6th GI-Conference on Theoretical Computer Science
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The first-value operator assigns to any sequence of partial functions of the same type a new such function. Its domain is the union of the domains of the sequence functions, and its value at any point is just the value of the first function in the sequence which is defined at that point. In this paper, the first-value operator is applied to establish hierarchies of classes of functions under various settings. For effective sequences of computable discrete functions, we obtain a hierarchy connected with Ershov's one within @D"2^0. The non-effective version over real functions is connected with the degrees of discontinuity and yields a hierarchy related to Hausdorff's difference hierarchy in the Borel class @D"2^B. Finally, the effective version over approximately computable real functions forms a hierarchy which provides a useful tool in computable analysis.