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Combinatorial Problems for Horn Clauses

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Graph Theory, Computational Intelligence and Thought

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5420))

Abstract

Given a family of Horn clauses, what is the minimal number of Horn clauses implying all other clauses in the family? What is the maximal number of Horn clauses from the family without having resolvents of a certain kind? We consider various problems of this type, and give some sharp bounds. We also consider the probability that a random family of a given size implies all other clauses in the family, and we prove the existence of a sharp threshold.

This material is based upon work supported by the National Science Foundation under Grants No. CCF-0431059 and DMS-0653946.

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Author information

Authors and Affiliations

  1. University of Illinois at Chicago, Chicago, IL, USA

    Marina Langlois, Dhruv Mubayi, Robert H. Sloan & György Turán

  2. Hungarian Academy of Sciences & University of Szeged, Hungary

    György Turán

Authors
  1. Marina Langlois
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  2. Dhruv Mubayi
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  3. Robert H. Sloan
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  4. György Turán
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Editor information

Editors and Affiliations

  1. The Caesarea Rothschild Institute, Mount Carmel, University of Haifa, 31905, Haifa, Israel

    Marina Lipshteyn

  2. Department of Computer Science and Mathematics, Ariel University Center of Samaria, 40700, Ariel, Israel

    Vadim E. Levit

  3. Department of Computer Science, Colorado State University, 80523-1873, Fort Collins, CO, USA

    Ross M. McConnell

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© 2009 Springer-Verlag Berlin Heidelberg

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Langlois, M., Mubayi, D., Sloan, R.H., Turán, G. (2009). Combinatorial Problems for Horn Clauses . In: Lipshteyn, M., Levit, V.E., McConnell, R.M. (eds) Graph Theory, Computational Intelligence and Thought. Lecture Notes in Computer Science, vol 5420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02029-2_6

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  • DOI: https://doi.org/10.1007/978-3-642-02029-2_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02028-5

  • Online ISBN: 978-3-642-02029-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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