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Nondeterministic functions and the existence of optimal proof systems

Beyersdorff, O, Koebler, J and Messner, J (2009) Nondeterministic functions and the existence of optimal proof systems. Theoretical Computer Science, 410 (38-40). 3839 - 3855 . ISSN 0304-3975

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We provide new characterizations of two previously studied questions on nondeterministic function classes: Q1: Do nondeterministic functions admit efficient deterministic refinements? Q2: Do nondeterministic function classes contain complete functions? We show that Q1 for the class is equivalent to the question whether the standard proof system for SAT is p-optimal, and to the assumption that every optimal proof system is p-optimal. Assuming only the existence of a p-optimal proof system for SAT, we show that every set with an optimal proof system has a p-optimal proof system. Under the latter assumption, we also obtain a positive answer to Q2 for the class . An alternative view on nondeterministic functions is provided by disjoint sets and tuples. We pursue this approach for disjoint -pairs and its generalizations to tuples of sets from and with disjointness conditions of varying strength. In this way, we obtain new characterizations of Q2 for the class . Question Q1 for is equivalent to the question of whether every disjoint -pair is easy to separate. In addition, we characterize this problem by the question of whether every propositional proof system has the effective interpolation property. Again, these interpolation properties are intimately connected to disjoint -pairs, and we show how different interpolation properties can be modeled by -pairs associated with the underlying proof system.

Item Type: Article
Copyright, Publisher and Additional Information: © 2009, Elsevier. This is an author produced version of a paper published in Theoretical Computer Science. Uploaded in accordance with the publisher's self-archiving policy.
Keywords: Optimal proof systems, Nondeterministic functions, 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: 13 Dec 2012 12:45
Last Modified: 09 Jun 2014 04:34
Published Version: http://dx.doi.org/10.1016/j.tcs.2009.05.021
Status: Published
Publisher: Elsevier
Identification Number: 10.1016/j.tcs.2009.05.021
URI: http://eprints.whiterose.ac.uk/id/eprint/74811

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