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 .
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.
|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:||25 Oct 2016 16:31|