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Efficient Recognition of Random Unsatisfiable k-SAT Instances by Spectral Methods

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STACS 2001 (STACS 2001)

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Abstract

It is known that random k-SAT instances with at least cn clauses where c = c k is a suitable constant are unsatisfiable (with high probability). We consider the problem to certify efficiently the unsatis- fiability of such formulas. A result of Beame et al. shows that k-SAT instances with at least n k-1= log n clauses can be certified unsatisfiable in polynomial time. We employ spectral methods to improve on this: We present a polynomial time algorithm which certifies random k-SAT instances for k even with at least 2k . (k/2)7 . (ln n)7 . n k/2 = n (k/2)+o(1) clauses as unsatisfiable (with high probability).

Partially supported by a USA-Israeli BSF grant.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Exact Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    Andreas Goerdt

  2. Fakultät für Informatik, TU Chemnitz, 09107, Chemnitz, Germany

    Michael Krivelevich

Authors
  1. Andreas Goerdt
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  2. Michael Krivelevich
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Editor information

Editors and Affiliations

  1. I3S & INRIA Sophia Antipolis INRIA, CNRS, 2004 Route des Lucioles, 06902, Sophia-Antipolis, France

    Afonso Ferreira

  2. Institut für Theoretische Informatik, Fakultät Informatik, TU Dresden, 01062, Dresden, Germany

    Horst Reichel

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© 2001 Springer-Verlag Berlin Heidelberg

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Goerdt, A., Krivelevich, M. (2001). Efficient Recognition of Random Unsatisfiable k-SAT Instances by Spectral Methods. In: Ferreira, A., Reichel, H. (eds) STACS 2001. STACS 2001. Lecture Notes in Computer Science, vol 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44693-1_26

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  • DOI: https://doi.org/10.1007/3-540-44693-1_26

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  • Print ISBN: 978-3-540-41695-1

  • Online ISBN: 978-3-540-44693-4

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