A Characterization of the Complexity of Resilience and Responsibility for Conjunctive Queries

Several research thrusts in the area of data management have focused on understanding how changes in the data affect the output of a view or standing query. Example applications are explaining query results, propagating updates through views, and anonymizing datasets. These applications usually rely on understanding how interventions in a database impact the output of a query. An important aspect of this analysis is the problem of deleting a minimum number of tuples from the input tables to make a given Boolean query false. We refer to this problem as “the resilience of a query” and show its connections to the well-studied problems of deletion propagation and causal responsibility. We thus study the complexity of resilience for self-join-free conjunctive queries, and also make several contributions to previous known results for the problems of deletion propagation with source side-effects and causal responsibility : (1) We define the notion of resilience and provide a complete dichotomy for the class of self-join-free conjunctive queries with arbitrary functional dependencies; this dichotomy also extends and generalizes previous tractability results on deletion propagation with source side-effects. (2) We formalize the connection between resilience and causal responsibility, and show that resilience has a larger class of tractable queries than responsibility. (3) We identify a mistake in a previous dichotomy for the problem of causal responsibility and offer a revised characterization based on new, simpler, and more intuitive notions. (4) Finally, we extend the dichotomy for causal responsibility in two ways: (a) we treat cases where the input tables contain functional dependencies, and (b) we compute responsibility for a set of tuples specified via wildcards.