Branching process approach for 2-sat thresholds

It is well known that, as n tends to∞, the probability of satisfiability for a random 2-SAT formula on n variables, where each clause occurs independently with probability α/2n, exhibits a sharp threshold at α = 1. We study a more general 2-SAT model in which each clause occurs independently but with probability αi/2n, where i ε {0, 1, 2} is the number of positive literals in that clause. We generalize the branching process arguments used byVerhoeven (1999) to determine the satisfiability threshold for this model in terms of the maximum eigenvalue of the branching matrix.