LIPIcs.FSTTCS.2014.445.pdf
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Separating Cook Completeness from Karp-Levin Completeness Under a Worst-Case Hardness Hypothesis
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- Publication date: 2014-12-12
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34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS)
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Debasis Mandal, A. Pavan, and Rajeswari Venugopalan. Separating Cook Completeness from Karp-Levin Completeness Under a Worst-Case Hardness Hypothesis. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 445-456, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2014)
https://doi.org/10.4230/LIPIcs.FSTTCS.2014.445
https://doi.org/10.4230/LIPIcs.FSTTCS.2014.445
Abstract
We show that there is a language that is Turing complete for NP but not many-one complete for NP, under a worst-case hardness hypothesis. Our hypothesis asserts the existence of a non-deterministic, double-exponential time machine that runs in time O(2^2^n^c) (for some c > 1) accepting Sigma^* whose accepting computations cannot be computed by bounded-error, probabilistic machines running in time O(2^2^{beta * 2^n^c) (for some beta > 0). This is the first result that separates completeness notions for NP under a worst-case hardness hypothesis.
Keywords
- Cook reduction
- Karp reduction
- NP-completeness
- Turing completeness
- many-one completeness
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