This paper gives a dichotomy theorem for the complexity of computing the partition\ud function of an instance of a weighted Boolean constraint satisfaction problem. The problem\ud is parameterized by a finite set F of nonnegative functions that may be used to assign weights to\ud the configurations (feasible solutions) of a problem instance. Classical constraint satisfaction problems\ud correspond to the special case of 0,1-valued functions. We show that computing the partition\ud function, i.e., the sum of the weights of all configurations, is FP#P-complete unless either (1) every\ud function in F is of “product type,” or (2) every function in F is “pure affine.” In the remaining cases,\ud computing the partition function is in P
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