The article focuses on the computation of expected Shapley-like scores of Boolean functions, which generalize the well-known Shapley and Banzhaf values from cooperative game theory to probabilistic settings. The authors first establish a connection between the complexity of computing expected Shapley-like scores and the computation of expected values of Boolean functions. They show that these two problems are interreducible in polynomial time, thus obtaining the same tractability landscape.
The authors then investigate a specific tractable case where Boolean functions are represented as deterministic decomposable circuits, and they design a polynomial-time algorithm for this setting. They present applications of their results to probabilistic databases through database provenance, and provide an effective implementation within the ProvSQL system, which is experimentally validated on a standard benchmark.
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