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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.


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
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Publisher statement:© 2011 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
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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