Beyersdorff, O (2008) Tuples of disjoint NP-sets. Theory of Computing Systems, 43 (2). 118 - 135 . ISSN 1432-4350
Abstract
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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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 |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 07 Aug 2012 13:18 |
Last Modified: | 01 Nov 2016 20:59 |
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 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:74444 |