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On the structure of polynomial time degrees

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STACS 84 (STACS 1984)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 166))

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Abstract

The main results of this paper are the following. 1) For both the polynomial time many-one and the polynomial time Turing degrees of recursive sets, every countable distributive lattice can be embedded in any interval of degrees. Furthermore, certain restraints — like preservation of the least or greatest element — can be imposed on the embeddings. 2) The upper semilattice of polynomial time many-one degrees is distributive, whereas that of the polynomial time Turing degrees is nondistributive. This gives the first (elementary) difference between the algebraic structures of p-many-one and p-Turing degrees, respectively.

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Authors and Affiliations

  1. Lehrstuhl für Informatik II, Universität Dortmund, D-4600, Dortmund 50, W.Germany

    Klaus Ambos-Spies

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  1. Klaus Ambos-Spies
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M. Fontet K. Mehlhorn

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© 1984 Springer-Verlag Berlin Heidelberg

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Ambos-Spies, K. (1984). On the structure of polynomial time degrees. In: Fontet, M., Mehlhorn, K. (eds) STACS 84. STACS 1984. Lecture Notes in Computer Science, vol 166. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12920-0_18

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  • DOI: https://doi.org/10.1007/3-540-12920-0_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12920-2

  • Online ISBN: 978-3-540-38805-0

  • eBook Packages: Springer Book Archive

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