Efficient decision procedures and computational complexity for IG and ICD

Develop efficient procedures for deciding graphical identifiability (IG) and identifiability by common derivation (ICD), and characterize the computational complexity of these decision problems for collections of causal graphs.

Background

The hierarchy established in the paper separates graph-based identifiability from derivation-based identifiability and shows that these notions can differ for collections of causal graphs. Although the paper provides structural relationships and counterexamples, it does not supply general efficient algorithms for deciding either notion.

The conclusion identifies both algorithmic development and complexity analysis as unresolved directions, motivated by the practical difficulty of checking validity uniformly across potentially large collections of compatible causal diagrams.

References

In particular, developing efficient procedures for deciding IG and ICD, and characterizing their computational complexity, remain open directions.

— Causal Effect Identifiability in Causal Abstractions: A Strict Hierarchy of Criteria  (2610.13520 - Yvernes et al., 9 Oct 2026) in Section 6, “Conclusion”