MSO2 models on bounded-treewidth graphs admit SDD representations of size linear in treewidth plus formula size and OBDD representations linear in pathwidth, with a matching lower bound showing OBDDs cannot be parameterized by treewidth alone.
Evaluation of an MSO-solver
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Parameterized Complexity Of Representing Models Of MSO Formulas
MSO2 models on bounded-treewidth graphs admit SDD representations of size linear in treewidth plus formula size and OBDD representations linear in pathwidth, with a matching lower bound showing OBDDs cannot be parameterized by treewidth alone.