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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Satisfiability Thresholds beyond k −XORSAT
verfasst von : Andreas Goerdt, Lutz Falke
Erschienen in: Computer Science – Theory and Applications
Verlag: Springer Berlin Heidelberg
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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.