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δ-Uniformly decidable sets and turing machines

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Fundamentals of Computation Theory (FCT 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1684))

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Abstract

We give a characterization of the archimedean fields in which nontrivial δ-uniform decidable sets exist. More exactly, after we introduce a notion of Turing closure of an archimedean field we prove that such a field posseses nontrivial δ-uniformly decidable sets if and only if it is not Turing closed. Moreover, if a function is δ-uniformly computable on a Turing closed field then it is rational over each of the connected components induced on the halting set by the reals. Finally, given a field which is not Turing closed, we obtain as a consequence that there exists a δ-uniform machine computing a total function which is not rational.

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Author information

Authors and Affiliations

  1. Department of Computer Science, West University of Timişoara, Bd. V. Pârvan nr. 4, 1900, Timişoara, Romania

    Adriana Popovici

  2. Department of Mathematics, West University of Timişoara, Bd. V. Pârvan nr. 4, 1900, Timişoara, Romania

    Dan Popovici

Authors
  1. Adriana Popovici
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  2. Dan Popovici
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science, “A.I.Cuza” University, 6600, Iaşi, Romania

    Gabriel Ciobanu

  2. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700, Bucharest, Romania

    Gheorghe Păun

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© 1999 Springer-Verlag Berlin Heidelberg

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Popovici, A., Popovici, D. (1999). δ-Uniformly decidable sets and turing machines. In: Ciobanu, G., Păun, G. (eds) Fundamentals of Computation Theory. FCT 1999. Lecture Notes in Computer Science, vol 1684. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48321-7_36

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  • DOI: https://doi.org/10.1007/3-540-48321-7_36

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66412-3

  • Online ISBN: 978-3-540-48321-2

  • eBook Packages: Springer Book Archive

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