On the computational complexity of read once resolution decidability in 2CNF formulas

Hans Kleine Büning; Piotr Wojciechowski; K. Subramani

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arXiv · 1610.04523

On the computational complexity of read once resolution decidability in 2CNF formulas

Hans Kleine Büning·Piotr Wojciechowski·K. Subramani

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Abstract

In this paper, we analyze 2CNF formulas from the perspectives of Read-Once resolution (ROR) refutation schemes. We focus on two types of ROR refutations, viz., variable-once refutation and clause-once refutation. In the former, each variable may be used at most once in the derivation of a refutation, while in the latter, each clause may be used at most once. We show that the problem of checking whether a given 2CNF formula has an ROR refutation under both schemes is NP-complete. This is surprising in light of the fact that there exist polynomial refutation schemes (tree-resolution and DAG-resolution) for 2CNF formulas. On the positive side, we show that 2CNF formulas have copy-complexity 2, which means that any unsatisfiable 2CNF formula has a refutation in which any clause needs to be used at most twice.

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Hans Kleine Büning, Piotr Wojciechowski, K. Subramani. 2016-10-14. On the computational complexity of read once resolution decidability in 2CNF formulas. https://arxiv.org/abs/1610.04523

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