The Limits of Tractability in Resolution-Based Propositional Proof Systems

Abstract

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On the complexity of resolution-based proof systems

“…In [21], Dantchev and Martin showed that if the relativization of the aforementioned least number principle, that is, the sentence expressing the principle for all non-empty subsets of the universe, can be interpreted in a first-order formula without finite models, then there are short R(const)-refutations of the propositional translations of that formula. The interpretations allowed are those in which relations and functions are expressed as Σ 1 -formulas except for the relativization relation, that is necessarily expressed as a quantifier-free formula.…”

“…We would be interested in determining the existence of a complete principle for the class of those whose propositional translations have polynomial-size R(const) refutations. In [21], Dantchev and Martin suggest that the relativization of the Least Number Principle could be a candidate for this role.…”