Abstract
This talk will present our results on how to efficiently enumerate the satisfying assignments of circuits in tractable knowledge compilation formalisms (structured d-DNNFs and variants). We will explain how these results can then be used to re-prove linear-preprocessing and output-linear delay enumeration of the satisfying assignments of Monadic Second-Order logic queries on trees, or the enumeration of the mappings of document spanners in database theory. We will also explain how these results allow for efficient updates to the underlying circuit, leading to results on efficiently maintaining enumeration structures on dynamic data.