For some methods, we show that there is a sharp increase in the size of the compact representation for a small increase in the size of the grammar, which gives us a strong indication of how difficult it would be to apply the method to much larger grammars.
1 Assume we have a list of subautomata A1 ..... Am that is ordered from lower-level to higher-level automata; i.e., if an automaton Ap occurs as the label of a transition of automaton Aq, then p < q; Am must be the start symbol S. This order is a natural result of the way that subautomata are constructed during our depth-first traversal of the grammar, which is actually postorder in the sense that a subautomaton is output after all subautomata occurring at its transitions have been output.