Separating the Notions of Self- and Autoreducibility

  • Piotr Faliszewski
  • Mitsunori Ogihara
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.


Turing Machine Recursive Call Recursion Tree Query String Oracle Query 
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 2005

Authors and Affiliations

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

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