Separating the Notions of Self- and Autoreducibility

  • Piotr Faliszewski
  • Mitsunori Ogihara
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3618)


Recently Glaßer et al. have shown that for many classes C including PSPACE and NP it holds that all of its nontrivial many-one complete languages are autoreducible. This immediately raises the question of whether all many-one complete languages are Turing self-reducible for such classes C.

This paper considers a simpler version of this question—whether all PSPACE-complete (NP-complete) languages are length-decreasing self-reducible. We show that if all PSPACE-complete languages are length-decreasing self-reducible then PSPACE = P and that if all NP-complete languages are length-decreasing self-reducible then NP = P.

The same type of result holds for many other natural complexity classes. In particular, we show that (1) not all NL-complete sets are logspace length-decreasing self-reducible, (2) unconditionally not all PSPACE-complete languages are logpsace length-decreasing self-reducible, and (3) unconditionally not all PSPACE-complete languages are polynomial-time length-decreasing self-reducible.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Piotr Faliszewski
    • 1
  • Mitsunori Ogihara
    • 1
  1. 1.Department of Computer ScienceUniversity of RochesterRochesterUSA

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