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The limits of tractability in Resolution-based propositional proof systems.

Dantchev, Stefan and Martin, Barnaby (2012) 'The limits of tractability in Resolution-based propositional proof systems.', Annals of pure and applied logic., 163 (3). pp. 656-668.

Abstract

We study classes of propositional contradictions based on the Least Number Principle (LNP) in the refutation system of Resolution and its generalisations with bounded conjunction, Res(k). We prove that any first-order sentence with no finite models that admits a Σ1 interpretation of the LNP, relativised to a set that is quantifier-free definable, generates a sequence of propositional contradictions that have polynomially-sized refutations in the system Res(k), for some k. When one considers the LNP with total order we demonstrate that a Π1 interpretation of this is sufficient to generate such a propositional sequence with polynomially-sized refutations in the system Res(k). On the other hand, we prove that a very simple first-order sentence that admits a Π1 interpretation of the LNP (with partial and not total order) requires exponentially-sized refutations in both Resolution and Res(k), for all constant k.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.apal.2011.11.001
Publisher statement:© 2011 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Date accepted:No date available
Date deposited:12 September 2017
Date of first online publication:03 December 2011
Date first made open access:No date available

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