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International Computer Science Symposium in Russia

CSR 2012: Computer Science – Theory and Applications pp 148–159Cite as

Satisfiability Thresholds beyond k −XORSAT

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7353))

Abstract

We consider random systems of equations x 1 + … + x k  = a, 0 ≤ a ≤ 2 which are interpreted as equations modulo 3. We show for k ≥ 15 that the satisfiability threshold of such systems occurs where the 2 −core has density 1. We show a similar result for random uniquely extendible constraints over 4 elements. Our results extend previous results of Dubois/Mandler for equations mod 2 and k = 3 and Connamacher/Molloy for uniquely extendible constraints over a domain of 4 elements with k = 3 arguments.

The proof is based on variance calculations, using a technique introduced by Dubois/Mandler. However, several additional observations (of independent interest) are necessary.

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Author information

Authors and Affiliations

  1. Fakultät für Informatik, Technische Universität Chemnitz, Straße der Nationen 62, 09107, Chemnitz, Germany

    Andreas Goerdt & Lutz Falke

Authors
  1. Andreas Goerdt
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  2. Lutz Falke
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Editor information

Editors and Affiliations

  1. Steklov Institute of Mathematics at St.Petersburg, 191023, St. Petersburg, Russia

    Edward A. Hirsch

  2. University of Turku, 20014, Turku, Finland

    Juhani Karhumäki  & Arto Lepistö  & 

  3. Lobachevky State University of Nizhni Novgorod, 603950, Niszhi Novgorod, Russia

    Michail Prilutskii

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Goerdt, A., Falke, L. (2012). Satisfiability Thresholds beyond k −XORSAT. In: Hirsch, E.A., Karhumäki, J., Lepistö, A., Prilutskii, M. (eds) Computer Science – Theory and Applications. CSR 2012. Lecture Notes in Computer Science, vol 7353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30642-6_15

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  • DOI: https://doi.org/10.1007/978-3-642-30642-6_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30641-9

  • Online ISBN: 978-3-642-30642-6

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