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International Symposium on Algorithms and Computation

ISAAC 2003: Algorithms and Computation pp 98–107Cite as

Infinitely-Often Autoreducible Sets

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2906))

Abstract

A set A is autoreducible if one can compute, for all x, the value A(x) by querying A only at places y ≠ x. Furthermore, A is infinitely-often autoreducible if, for infinitely many x, the value A(x) can be computed by querying A only at places y ≠ x. For all other x, the computation outputs a special symbol to signal that the reduction is undefined. It is shown that for polynomial time Turing and truth-table autoreducibility there are sets A, B, C in EXP such that A is not infinitely-often Turing autoreducible, B is Turing autoreducible but not infinitely-often truth-table autoreducible, C is truth-table autoreducible with g(n)+ 1 queries but not infinitely-often Turing autoreducible with g(n) queries. Here n is the length of the input, g is nondecreasing and there exists a polynomial p such that p(n) bounds both, the computation time and the value, of g at input of length n. Furthermore, connections between notions of infinitely-often autoreducibility and notions of approximability are investigated. The Hausdorff-dimension of the class of sets which are not infinitely-often autoreducible is shown to be 1.

For the complete version of this paper, see reference [7].

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Author information

Authors and Affiliations

  1. Department of Computer and Information Sciences, Temple University, Wachman Hall (038-24), 1805 North Broad Street, Philadelphia, PA, 19122-6094, USA

    Richard Beigel

  2. NEC Laboratories America, 4 Independence Way, Princeton, NJ, 08540, USA

    Lance Fortnow

  3. Mathematisches Institut, Universität Heidelberg, Im Neuenheimer Feld 294, 69120, Heidelberg, EU, Germany

    Frank Stephan

Authors
  1. Richard Beigel
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  2. Lance Fortnow
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  3. Frank Stephan
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Editor information

Editors and Affiliations

  1. School of Science and Technology, Kwansei Gakuin University, Sanda, Japan

    Toshihide Ibaraki

  2. Department of Architecture and Architectural Engineering, Kyoto University, 615-8540, Nishikyo-ku, Kyoto, Japan

    Naoki Katoh

  3. Department of Computer Science and Communication Engineering, Kyushu University, 812-8581, Fukuoka, Japan

    Hirotaka Ono

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© 2003 Springer-Verlag Berlin Heidelberg

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Beigel, R., Fortnow, L., Stephan, F. (2003). Infinitely-Often Autoreducible Sets. In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_12

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  • DOI: https://doi.org/10.1007/978-3-540-24587-2_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20695-8

  • Online ISBN: 978-3-540-24587-2

  • eBook Packages: Springer Book Archive

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