In a pushdown automaton P=(Q,Σ,Γ,δ,q0,F), a transition of the form,
where p,q∈Q, a∈σ∪{ϵ}, X,Y,∈Γ∪{ϵ}, represents
(q,Y) ∈ δ(p,a,X)
Consider the following pushdown automaton over the input alphabet Σ={a,b} and stack alphabet Γ={#,A}.
The number of strings of length 100 accepted by the above pushdown automaton is ___________ .
(A) 50
(B) 100
(C) 55
(D) 45
Answer: (A)
Explanation: According to given question,
L = {anbm| n>m & n+m=100} L = a51b49,…..,a99b,a100 |L| = 50
For reaching q3 from q2 there must be “A” on the top of the stack, hence n>m.
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