The limits of tractability in resolution-based propositional proof systems

Dantchev, Stefan and Martin, Barnaby (2010) The limits of tractability in resolution-based propositional proof systems. In: 6th International Conference on Computability in Europe: Programs, Proofs, Processes (CIE 2010), 30 June - 4 July 2010, Portugal.

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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 Resolution.

Item Type: Conference or Workshop Item (Paper)
Research Areas: A. > School of Science and Technology > Computer Science
A. > School of Science and Technology > Computer Science > Foundations of Computing group
Item ID: 9677
Useful Links:
Depositing User: Devika Mohan
Date Deposited: 16 Jan 2013 08:49
Last Modified: 24 Apr 2018 15:21
URI: http://eprints.mdx.ac.uk/id/eprint/9677

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