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Tuples of disjoint NP-sets

Beyersdorff, O (2008) Tuples of disjoint NP-sets. Theory of Computing Systems, 43 (2). 118 - 135 . ISSN 1432-4350

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Disjoint NPUnknown control sequence '\mathsf' -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 NPUnknown control sequence '\mathsf' -pairs to disjoint k-tuples of NPUnknown control sequence '\mathsf' -sets for k≥2. We define subclasses of the class of all disjoint k-tuples of NPUnknown control sequence '\mathsf' -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 NPUnknown control sequence '\mathsf' -pairs exist if and only if complete disjoint k-tuples of NPUnknown control sequence '\mathsf' -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: Article
Copyright, Publisher and Additional Information: © 2008, Springer Verlag. This is an author produced version of a paper published in Theory of Computing Systems. Uploaded in accordance with the publisher's self-archiving policy. The original publication is available at www.springerlink.com
Keywords: propositional proof systems, disjoint NP-pairs
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 07 Aug 2012 13:18
Last Modified: 09 Jun 2014 10:33
Published Version: http://dx.doi.org/10.1007/s00224-007-9023-8
Status: Published
Publisher: Springer Verlag
Identification Number: 10.1007/s00224-007-9023-8
URI: http://eprints.whiterose.ac.uk/id/eprint/74444

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