The Computational Complexity of Structure-Based Causality
This work addresses foundational complexity issues in causality theory, which is incremental as it builds on prior definitions and results.
The paper tackles the computational complexity of determining actual causality under a modified definition by Halpern and Pearl, showing it is D_2^P-complete, and extends this to characterize complexity for responsibility and blame.
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.