Thus, we use the following transitions: The following transitions handle the special case of a treelet consisting of a single node: Once M has been constructed from M, we can process each input DAG D by converting it into a binary DAG D and then by running M on D using Algorithm 2.
as with the algorithm of Section 6 for non-extended DAGs, the running time is exponential in the treewidth of the input DAG, linear in the total size of the input DAG, and, for a fixed treewidth, polynomial in the number of states of the extended automaton and in the number of states of the largest m-automaton A σ for the transitions on a single input symbol σ.