List of top Theory of Computation Questions on Context-free grammars and push-down automata

Consider the following context-free grammar \(G\), where \(S\), \(A\), and \(B\) are the variables (non-terminals), \(a\) and \(b\) are the terminal symbols, \(S\) is the start variable, and the rules of \(G\) are described as:
\[ S \to aaB \mid Abb \] \[ A \to a \mid AaA \] \[ B \to b \mid bB \] Which ONE of the languages \(L(G)\) is accepted by \(G\)?

For a string \(w\), we define \(w^R\) to be the reverse of \(w\). Which of the following languages is/are context-free?

In a pushdown automaton \( P = (Q, \Sigma, \Gamma, \delta, q_0, F) \), a transition of the form

where \( p, q \in Q \), \( a \in \Sigma \cup \{\epsilon\} \), and \( X, Y \in \Gamma \cup \{\epsilon\} \), represents \[ (q, Y) \in \delta(p, a, X). \] Consider the following pushdown automaton over the input alphabet \( \Sigma = \{a, b\} \) and stack alphabet \( \Gamma = \{\#, A\} \):

The number of strings of length 100 accepted by the above pushdown automaton is \(\underline{\hspace{2cm}}\).