We determine the exact freezing threshold, r f , for a family of models of random boolean constraint satisfaction problems, including NAE-SAT and hypergraph 2-colouring, when the constraint size is sufficiently large. If the constraint-density of a random CSP, F , in our family is greater than r f then for almost every solution of F , a linear number of variables are frozen, meaning that their colours cannot be changed by a sequence of alterations in which we change o(n) variables at a time, always switching to another solution. If the constraint-density is less than r f , then almost every solution has o(n) frozen variables.
REF studied a a broad range of boolean constraint satisfaction problems, including hypergraph 2-colouring.
Frozen variables in random boolean constraint satisfaction problems
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Computer Science Mathematics