# Why don't we use $as end marker for input in PDA? I am reading Theory of Computation by Peter Linz. The transitions for PDA uses$\epsilon$as end marker for input string. For example if the final state is$q_1$then the transition is written like$\delta(q_0,\epsilon,z)=(q_1,z)$. Why don't they write the transition as$\delta(q_0,\$,z)=(q_1,z)$.

• We want to have possibility to allow stack to become empty without going to final state. – Szymon Stankiewicz Nov 4 '17 at 17:02
• $\epsilon$ is not a "marker". – rici Nov 4 '17 at 17:11
• @rici I know it's not a marker. But they are treating it like a marker. – Kishan Kumar Nov 4 '17 at 17:18
• @KishanKumar If they did that, it would be wrong. An $\varepsilon$-transition can trigger at any point in time, not only at the end of the input. – Raphael Nov 4 '17 at 19:16
• $\$\$ is the "bottom of stack" marker. You can't introduce "end of input" markers without changing the input language (making it prefix-free). – Raphael Nov 4 '17 at 19:17