Minimum Witnesses for Unsatisfiable 2CNFs

  • Joshua Buresh-Oppenheim
  • David Mitchell
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4121)

Abstract

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.

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References

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    Subramani, K.: Optimal length tree-like resolution refutations for 2SAT formulas. ACM Transactions on Computational Logic 5(2), 316–320 (2004)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Joshua Buresh-Oppenheim
    • 1
  • David Mitchell
    • 1
  1. 1.Simon Fraser University 

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