Dempster's Rule of Combination is #P-Complete

Abstract We consider the complexity of combining bodies of evidence according to the rules of the Dempster-Shafer theory of evidence. We prove that, given as input a set of tables representing basic probability assignments m 1 , …, m n over a frame of discernment Θ, and a set A ⊆ Θ , the problem of computing the combined basic probability value (m 1 ⊕ … ⊕ m n )(A) is # P -complete. As a corollary, we obtain that while the simple belief, plausibility, and commonality values Bel (A), Pl (A), and Q(A) can be computed in polynomial time, the problems of computing the combinations (Bel 1 ⊕ … ⊕ Bel n (A), (Pl 1 ⊕ … ⊕ Pl n )(A), and (Q 1 ⊕ … ⊕ Q n )(A) are # P -complete.

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