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GATE CS 2021 Set 1 — Question 61

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NAT+2 / -0HardPushdown Automata (PDA)Context-Free LanguagesTheory of Computation

Theory of Computation → Context-Free Languages → Pushdown Automata (PDA)

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Question

In a pushdown automaton P=(Q,Σ,Γ,δ,q0,F)P = (Q, \Sigma, \Gamma, \delta, q_0, F), a transition of the form,
where p,q∈Qp, q \in Q, a∈Σ∪{ϵ}a \in \Sigma \cup \{\epsilon\}, and X,Y∈Γ∪{ϵ}X, Y \in \Gamma \cup \{\epsilon\}, represents(q,Y)∈δ(p,a,X).(q, Y) \in \delta(p, a, X).Consider the following pushdown automaton over the input alphabet Σ={a,b}\Sigma = \{a, b\} and stack alphabet Γ={#,A}\Gamma = \{\#, A\}.
The number of strings of length 100 accepted by the above pushdown automaton is __________.
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