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Tuples of disjoint NP-sets

Beyersdorff, O (2006) Tuples of disjoint NP-sets. In: Grigoriev, D, Harrison, J and Hirsch, EA, (eds.) Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). First International Computer Science Symposium in Russia, 8-12 June 2006, St Petersburg, Russia. Lecture Notes in Computer Science, Lectur (3967). Springer Verlag , 80 - 91 .

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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.

Item Type: Proceedings Paper
Copyright, Publisher and Additional Information: © 2006, Springer Verlag. This is an author produced version of a paper published in Lecture Notes in Computer Science. Uploaded in accordance with the publisher's self-archiving policy. The original publication is available at www.springerlink.com
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 10 Dec 2012 12:29
Last Modified: 08 Jun 2014 20:15
Published Version: http://dx.doi.org/10.1007/11753728_11
Status: Published
Publisher: Springer Verlag
Identification Number: 10.1007/11753728_11
URI: http://eprints.whiterose.ac.uk/id/eprint/74800

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