Short Proofs Without New Variables

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10395)


Adding and removing redundant clauses is at the core of state-of-the-art SAT solving. Crucial is the ability to add short clauses whose redundancy can be determined in polynomial time. We present a characterization of the strongest notion of clause redundancy (i.e., addition of the clause preserves satisfiability) in terms of an implication relationship. By using a polynomial-time decidable implication relation based on unit propagation, we thus obtain an efficiently checkable redundancy notion. A proof system based on this notion is surprisingly strong, even without the introduction of new variables—the key component of short proofs presented in the proof complexity literature. We demonstrate this strength on the famous pigeon hole formulas by providing short clausal proofs without new variables.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceThe University of Texas at AustinAustinUSA
  2. 2.Institute of Information SystemsVienna University of TechnologyViennaAustria
  3. 3.Institute for Formal Models and VerificationJKU LinzLinzAustria

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