LIPIcs.STACS.2016.42.pdf
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Autoreducibility of NP-Complete Sets
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33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS) - License:
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- Publication Date: 2016-02-16
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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
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.
Keywords
- computational complexity
- NP-completeness
- autoreducibility
- genericity
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References
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