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, 08-12 Jun 2006, St Petersburg, Russia. Lecture Notes in Computer Science, Lectur (3967). Springer Verlag , 80 - 91 .
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.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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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 |
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) > Institute for Computational and Systems Science (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 10 Dec 2012 12:29 |
Last Modified: | 19 Dec 2022 13:24 |
Published Version: | http://dx.doi.org/10.1007/11753728_11 |
Status: | Published |
Publisher: | Springer Verlag |
Series Name: | Lecture Notes in Computer Science |
Identification Number: | 10.1007/11753728_11 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:74800 |