  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\
Sigma_2^P-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 by Hopkins and Pearl. As we show, this modification
has a nontrivial impact on the complexity of computing actual cause. To
characterize the complexity, a new family D_k^P, k= 1, 2, 3, ..., of complexity
classes is introduced, which generalizes the class DP introduced by
Papadimitriou and Yannakakis (DP is just D_1^P). %joe2 %We show that the
complexity of computing causality is $\D_2$-complete %under the new definition.
Chockler and Halpern \citeyear{CH04} extended the We show that the complexity
of computing causality under the updated definition is $D_2^P$-complete.
  Chockler and Halpern extended the definition of causality by introducing
notions of responsibility and blame. The complexity of determining the degree
of responsibility and blame using the original definition of causality was
completely characterized. Again, we show that changing the definition of
causality affects the complexity, and completely characterize it using the
updated definition.
