Lifted inference allows to perform inference in polynomial time w.r.t. domain sizes. For a lifted algorithm, completeness investigates model classes for which the algorithm is guaranteed to compute a lifted solution. We contribute, to the best of our knowledge, the first completeness and complexity analysis for a temporal lifted algorithm, the so-called lifted dynamic junction tree algorithm (LDJT). To treat time as a first class citizen, LDJT introduces some constraints. Given these constraints, we analyse the classes of liftable models. Further, we show that LDJT has many advantages from a complexity point of view compared to a propositional temporal inference algorithm w.r.t. domain sizes. Therefore, LDJT advances the number of models for which inference tasks can be solved in reasonable time not only from a practically point of view, but also from a theoretical point of view.
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