Satisfiability Thresholds beyond k −XORSAT

  • Andreas Goerdt
  • Lutz Falke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7353)


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.


Threshold Density Laplace Method Local Limit Theorem Sharp Threshold Equation Modulo 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Andreas Goerdt
    • 1
  • Lutz Falke
    • 1
  1. 1.Fakultät für InformatikTechnische Universität ChemnitzChemnitzGermany

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