Separating Cook Completeness from Karp-Levin Completeness Under a Worst-Case Hardness Hypothesis

Authors Debasis Mandal, A. Pavan, Rajeswari Venugopalan

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Debasis Mandal
A. Pavan
Rajeswari Venugopalan

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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)


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.
  • Cook reduction
  • Karp reduction
  • NP-completeness
  • Turing completeness
  • many-one completeness


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