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Prior research has focused on intra-domain fault localization leaving the cross-domain problem largely unaddressed. Faults often have widespread effects, which if correlated, could significantly improve fault localization. Past efforts rely on probing techniques or assume hierarchical domain structures; however, administrators are often unwilling to share network structure and state and domains are organized and connected in complex ways. We present an inference-graph-digest based formulation of the problem. The formulation not only explicitly models the inference accuracy and privacy requirements for discussing and reasoning over cross-domain problems, but also facilitates the re-use of existing fault localization algorithms while enforcing domain privacy policies. We demonstrate our formulation by deriving a cross-domain version of SHRINK, a recent probabilistic fault localization strategy.