Consider the NPDA $$ \left \langle Q= \left \{ q_{0}, q_{1}, q_{2} \right \},\Sigma = \left \{ 0, 1 \right \}, \Gamma = \left \{ 0, 1, \perp \right \}, \delta, q_{0}, \perp, F =\left \{ q_{2} \right \} \right \rangle $$, where (as per usual convention) $Q$ is the set of states, $\Sigma$ is the input alphabet, $\Gamma $ is the stack alphabet, $\delta $ is the state transition function $q_{0}$ is the initial state, $\perp $ is the initial stack symbol, and $F$ is the set of accepting states. The state transition is as follows:
Which one of the following sequences must follow the string $101100$ so that the overall string is accepted by the automaton?
- $10110$
- $10010$
- $01010$
- $01001$