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Does Advice Help to Prove Propositional Tautologies?

Beyersdorff, O and Mueller, S (2009) Does Advice Help to Prove Propositional Tautologies? In: Kullmann, O, (ed.) Theory and Applications of Satisfiability Testing SAT 2009. 12th International Conference, SAT 2009, 30 June - 3 July 2009, Swansea, UK. Lecture Notes in Computer Science, 5584 (Lectur). Springer Verlag , 65 - 72 . ISBN 978-3-642-02776-5

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Abstract

One of the starting points of propositional proof complexity is the seminal paper by Cook and Reckhow [6], where they defined propositional proof systems as poly-time computable functions which have all propositional tautologies as their range. Motivated by provability consequences in bounded arithmetic, Cook and Krajíček [5] have recently started the investigation of proof systems which are computed by poly-time functions using advice. While this yields a more powerful model, it is also less directly applicable in practice. In this note we investigate the question whether the usage of advice in propositional proof systems can be simplified or even eliminated. While in principle, the advice can be very complex, we show that proof systems with logarithmic advice are also computable in poly-time with access to a sparse NP-oracle. In addition, we show that if advice is ”not very helpful” for proving tautologies, then there exists an optimal propositional proof system without advice. In our main result, we prove that advice can be transferred from the proof to the formula, leading to an easier computational model. We obtain this result by employing a recent technique by Buhrman and Hitchcock [4].

Item Type: Proceedings Paper
Copyright, Publisher and Additional Information: © 2009, Springer Verla. This is an author produced version of a paper published in Theory and Applications of Satisfiability Testing SAT 2009. 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 14:29
Last Modified: 09 Jun 2014 10:38
Published Version: http://dx.doi.org/10.1007/978-3-642-02777-2_8
Status: Published
Publisher: Springer Verlag
Identification Number: 10.1007/978-3-642-02777-2_8
URI: http://eprints.whiterose.ac.uk/id/eprint/74803

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