Minimum Propositional Proof Length is NP-Hard to Linearly Approximate
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Optimal length tree-like resolution refutations for 2SAT formulas
ACM Transactions on Computational Logic (TOCL)
Redundancy in logic II: 2CNF and Horn propositional formulae
Artificial Intelligence
Minimum 2CNF resolution refutations in polynomial time
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Computation of renameable Horn backdoors
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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We consider the problem of finding the smallest proof of unsatisfiability of a 2CNF formula. In particular, we look at Resolution refutations and at minimum unsatisfiable subsets of the clauses of the CNF. We give a characterization of minimum tree-like Resolution refutations that explains why, to find them, it is not sufficient to find shortest paths in the implication graph of the CNF. The characterization allows us to develop an efficient algorithm for finding a smallest tree-like refutation and to show that the size of such a refutation is a good approximation to the size of the smallest general refutation. We also give a polynomial time dynamic programming algorithm for finding a smallest unsatisfiable subset of the clauses of a 2CNF.