Regulated Nondeterminism in Pushdown Automata: The Non-Regular Case

We continue the investigation of pushdown automata which are allowed to make a nondeterministic decision if and only if their pushdown content forms a string belonging to a given control language. We prove that if the control language is linear and non-regular, then the power of pushdown automata regulated in this way is increased to the power of Turing machines. From a practical point of view, however, it is inefficient to check the form of the pushdown content in each computational step. Therefore, we prove that only two checks of the pushdown content are of interest for these machines to be computationally complete. Based on this observation, we introduce and discuss a new model of regulated pushdown automata.