title: Can every DFA be simulated by a PDA?
body: <p>Given a Deterministic Finite Automata (DFA) M_1, does there always exist a Pushdown Automata (PDA) M_2 that accepts the same language as M_1?  I.e. <strong>can any DFA be simulated by a PDA?</strong>  Intuitively, it makes sense to me that a PDA is more powerful since it has an arbitrary amount of memory and can therefore accept more languages than a DFA, but how could this be formally proven?</p>