On Determining the Minimum Length, Tree-Like Resolution Refutation of 2SAT, and Extended 2SAT Formulas
This paper is concerned with the design of polynomial time algorithms to determine the shortest length, tree-like resolution refutation proofs for 2SAT and Q2SAT (Quantified 2SAT) clausal systems. Determining the shortest length resolution refutation has been shown to be NP-complete, even for HornSAT systems (for both tree-like and dag-like proofs); in fact obtaining even a linear approximation for such systems is NP-Hard. In this paper we demonstrate the existence of simple and efficient algorithms for the problem of determining the exact number of steps in the minimum length tree-like resolution refutation proof of a 2SAT or Q2SAT clausal system. To the best of our knowledge, our results are the first of their kind.
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