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We show new limits on the efficiency of using current techniques to makeexact probabilistic inference for large classes of natural problems. Inparticular we show new lower bounds on knowledge compilation to SDD and DNNFforms. We give strong lower bounds on the complexity of SDD representations byrelating SDD size to best-partition communication complexity. We use thisrelationship to prove exponential lower bounds on the SDD size for representinga large class of problems that occur naturally as queries over probabilisticdatabases. A consequence is that for representing unions of conjunctivequeries, SDDs are not qualitatively more concise than OBDDs. We also derivesimple examples for which SDDs must be exponentially less concise than FBDDs.Finally, we derive exponential lower bounds on the sizes of DNNFrepresentations using a new quasipolynomial simulation of DNNFs bynondeterministic FBDDs.

New Limits for Knowledge Compilation and Applications to Exact Model Counting