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Tuples of Disjoint NP-Sets

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Computer Science – Theory and Applications (CSR 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3967))

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Abstract

Disjoint NP-pairs are a well studied complexity theoretic concept with important applications in cryptography and propositional proof complexity. In this paper we introduce a natural generalization of the notion of disjoint NP-pairs to disjoint k-tuples of NP-sets for k ≥ 2. We define subclasses of the class of all disjoint k-tuples of NP-sets. These subclasses are associated with a propositional proof system and possess complete tuples which are defined from the proof system.

In our main result we show that complete disjoint NP-pairs exist if and only if complete disjoint k-tuples of NP-sets exist for all k ≥ 2. Further, this is equivalent to the existence of a propositional proof system in which the disjointness of all k-tuples is shortly provable. We also show that a strengthening of this conditions characterizes the existence of optimal proof systems.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Humboldt-Universität zu Berlin, 10099, Berlin, Germany

    Olaf Beyersdorff

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  1. Olaf Beyersdorff
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Editor information

Editors and Affiliations

  1. IRMAR, Université de Rennes, Campus de Beaulieu, 35042, Rennes Cedex, France

    Dima Grigoriev

  2. Intel Corporation, JF1-13, 2111 NE 25th Avenue, 97124, Hillsboro, OR, USA

    John Harrison

  3. Steklov Institute of Mathematics at St. Petersburg, 27 Fontanka, St., 191023, Petersburg, Russia

    Edward A. Hirsch

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© 2006 Springer-Verlag Berlin Heidelberg

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Beyersdorff, O. (2006). Tuples of Disjoint NP-Sets. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds) Computer Science – Theory and Applications. CSR 2006. Lecture Notes in Computer Science, vol 3967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11753728_11

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  • DOI: https://doi.org/10.1007/11753728_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34166-6

  • Online ISBN: 978-3-540-34168-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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