Exact thresholds for DPLL on random XOR-SAT and NP-complete extensions of XOR-SAT
Theoretical Computer Science
The freezing threshold for k-colourings of a random graph
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
A general model and thresholds for random constraint satisfaction problems
Artificial Intelligence
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We consider random instances of constraint satisfaction problems where each variable has domain size $d$ and each constraint contains $t$ restrictions on $k$ variables. For each $(d,k,t)$ we determine whether the resolution complexity is a.s. constant, polynomial, or exponential in the number of variables. For a particular range of $(d,k,t)$, we determine a sharp threshold for resolution complexity where the resolution complexity drops from a.s. exponential to a.s. polynomial when the clause density passes a specific value.