A direct construction of finite state automata for pushdown store languages

We provide a new construction of a nondeterministic finite automaton (NFA) accepting the pushdown store language of a given pushdown automaton (PDA). The resulting NFA has a number of states which is quadratic in the number of states and linear in the number of pushdown symbols of the given PDA. Moreover, we prove the size optimality of our construction. Beside improving some results in the literature, our approach represents an alternative and more direct proof of pushdown store language regularity. Finally, we give a characterization of the class of pushdown store languages.