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CPC
2016

The Satisfiability Threshold for k-XORSAT

4 years 3 months ago
The Satisfiability Threshold for k-XORSAT
We consider “unconstrained” random k-XORSAT, which is a uniformly random system of m linear non-homogeneous equations in F2 over n variables, each equation containing k ≥ 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 threshold for unconstrained 3-XORSAT. We show that m/n = 1 remains a sharp threshold for satisfiability of constrained k-XORSAT for every k ≥ 3, and we use standard results on the 2-core of a random k-uniform hypergraph to extend this result to find the threshold for unconstrained k-XORSAT. For constrained kXORSAT we narrow the phase transition window, showing that m−n → −∞ implies almost-sure satisfiability, while m−n → +∞ implies almostsure unsatisfiability.
Boris Pittel, Gregory B. Sorkin
Added 01 Apr 2016
Updated 01 Apr 2016
Type Journal
Year 2016
Where CPC
Authors Boris Pittel, Gregory B. Sorkin
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