# The Satisfiability Threshold for $k$-XORSAT, using an alternative proof

@article{Pittel2012TheST, title={The Satisfiability Threshold for \$k\$-XORSAT, using an alternative proof}, author={Boris G. Pittel and Gregory B. Sorkin}, journal={arXiv: Combinatorics}, year={2012} }

We consider "unconstrained" random $k$-XORSAT, which is a uniformly random system of $m$ linear non-homogeneous equations in $\mathbb{F}_2$ over $n$ variables, each equation containing $k \ge 3$ variables, and also consider a "constrained" model where every variable appears in at least two equations. Dubois and Mandler proved that $m/n=1$ is a sharp threshold for satisfiability of constrained 3-XORSAT, and analyzed the 2-core of a random 3-uniform hypergraph to extend this result to find the… Expand

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