The computational complexity of structure-based causality

Abstract

Halpern and Pearl introduced a definition of actual causality; Eiter and Lukasiewicz showed that computing whether X = x is a cause of Y = y is NP-complete in binary models (where all variables can take on only two values) and ΣP2 -complete in general models. In the final version of their paper, Halpern and Pearl slightly modified the definition of actual cause, in order to deal with problems pointed out by Hopkins and Pearl. As we show, this modification has a nontrivial impact on the complexity of computing whether →X = →x is a cause of Y = y. To characterize the complexity, a new family DPk , k = 1; 2; 3; ⋯, of complexity classes is introduced, which generalizes the class DP introduced by Papadimitriou and Yannakakis (DP is just DP1 ).We show that the complexity of computing causality under the updated definition is DP 2 -complete. Chockler and Halpern extended the definition of causality by introducing notions of responsibility and blame, and characterized the complexity of determining the degree of responsibility and blame using the original definition of causality. Here, we completely characterize the complexity using the updated definition of causality. In contrast to the results on causality, we show that moving to the updated definition does not result in a difference in the complexity of computing responsibility and blame.