Recognition of directed acyclic graphs by spanning tree automata

In this paper, we study tree automata for directed acyclic graphs (DAGs). We define the movement of a tree automaton on a DAG so that a DAG is accepted by a tree automaton if and only if the DAG has a spanning tree accepted by the tree automaton. We call this automaton a spanning tree automaton. The NP-completeness of the membership problem of DAGs for spanning tree automata is shown. However, if inputs are restricted to series–parallel graphs or generalized series–parallel graphs, it is shown that the membership problem for spanning tree automata is solvable in linear time.