Satisfiability thresholds beyond k-XORSAT
Discrete Mathematics
2011-12-12 v1
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. Our proof technique is based on variance calculations, using a technique introduced Dubois/Mandler. However, several additional observations (of independent interest) are necessary.
Cite
@article{arxiv.1112.2118,
title = {Satisfiability thresholds beyond k-XORSAT},
author = {Andreas Goerdt and Lutz Falke},
journal= {arXiv preprint arXiv:1112.2118},
year = {2011}
}