Sciweavers

CIE
2010
Springer

The Limits of Tractability in Resolution-Based Propositional Proof Systems

13 years 5 months ago
The Limits of Tractability in Resolution-Based Propositional Proof Systems
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 1 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 1 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 1 interpretation of the LNP (with partial and not total order) requires exponentially-sized refutations in Resolution.
Stefan S. Dantchev, Barnaby Martin
Added 25 Oct 2010
Updated 25 Oct 2010
Type Conference
Year 2010
Where CIE
Authors Stefan S. Dantchev, Barnaby Martin
Comments (0)