Parameterized Complexity Of Representing Models Of MSO Formulas

ArXi:2604.08707v1 Announce Type: new Monadic second order logic (MSO2) plays an important role in parameterized complexity due to the Courcelle's theorem. This theorem states that the problem of checking if a given graph has a property specified by a given MSO2 formula can be solved by a parameterized linear time algorithm with respect to the treewidth of the graph and the size of the formula. We extend this result by showing that models of MSO2 formula with free variables can be represented with a decision diagram whose size is parameterized linear in the above mentioned parameter.