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The degree structure of 1-L reductions

  • Hans-Jörg Burtschick
  • Albrecht Hoene
Communications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 629)

Abstract

A 1-L function is one that is computable by a logspace Turing machine that moves its input head only in one direction. We show that there exist 1-L complete sets for PSPACE that are not 1-L isomorphic. In other words, the 1-L complete degree for PSPACE does not collapse. This contrasts a result of Allender who showed that all 1-L complete sets for PSPACE are polynomial-time isomorphic. Since all 1-L complete sets for PSPACE are equivalent under 1-L reductions that are one-one and quadratically length-increasing this also provides an example of a ≤ 1,qli 1−L -degree that does not collapse to a single 1-L isomorphism type.

Relatedly, we prove that there exist two sets A and B that are ≤ 1 1−L equivalent but not ≤ 1honest 1−L equivalent. That is, there is a one-one 1-L degree that is no honest one-one 1-L degree.

Keywords

Turing Machine Random Oracle Isomorphism Type Input Tape Logarithmic Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Hans-Jörg Burtschick
    • 1
  • Albrecht Hoene
    • 1
  1. 1.Fachbereich InformatikTechnische Universität BerlinBerlin 10Germany

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