The degree structure of 1-L reductions

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


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.


Turing Machine Random Oracle Isomorphism Type Input Tape Logarithmic Space 
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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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