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Autoreducibility of NP-Complete Sets

Authors John M. Hitchcock, Hadi Shafei

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John M. Hitchcock
Hadi Shafei

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John M. Hitchcock and Hadi Shafei. Autoreducibility of NP-Complete Sets. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 42:1-42:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.STACS.2016.42

Abstract

We study the polynomial-time autoreducibility of NP-complete sets and obtain separations under strong hypotheses for NP. Assuming there is a p-generic set in NP, we show the following:

- For every k >= 2, there is a k-T-complete set for NP that is k-T autoreducible, but is not k-tt autoreducible or (k-1)-T autoreducible.

- For every k >= 3, there is a k-tt-complete set for NP that is k-tt autoreducible, but is not (k-1)-tt autoreducible or (k-2)-T autoreducible.

- There is a tt-complete set for NP that is tt-autoreducible, but is not btt-autoreducible.
  
Under the stronger assumption that there is a p-generic set in NP cap coNP, we show:

- For every k >= 2, there is a k-tt-complete set for NP that is k-tt autoreducible, but is not (k-1)-T autoreducible.
  
Our proofs are based on constructions from separating NP-completeness notions. For example, the construction of a 2-T-complete set for NP that is not 2-tt-complete also separates 2-T-autoreducibility from 2-tt-autoreducibility.

Subject Classification

Keywords
  • computational complexity
  • NP-completeness
  • autoreducibility
  • genericity

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References

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