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Options:

$\left \{ \left ( b^{n}ab^{n}a\right )^{m} | n,m \geq 0 \right \}$

$\left \{ \left ( b^{n}ab^{n}a\right )^{m} | n,m \geq 0 \right \} \cup \left \{ b^{n} | n\geq 0 \right \}$

$\left \{ \left ( b^{n}ab^{n}\right )^{m}a | n,m \geq 0 \right \}$

$NONE$

edited | 138 views
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is it none?
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Option C
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I am getting none but answer given is A
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Is it A?
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The above PDA accepts by emptying the stack.So you push N b's onto the stack and then on seeing an a move to q1.In q1 pop each time for input b and if N b's are there then only z0 would be left on the stack.So on seeing an a move to z0.If the string is completely parsed then on seeing epsilon stack would be emptied and string would be accepted.Else the process could repeat again.So the language is of the form {(b^n a b^n a)^m|n,m>=0].
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string 'aa' is generated by option A..is it accepted by PDA ?
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Correct answer is D, it will updated by them.
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Yes it is accepted by the above PDA.On seeing a go to q1 and then on seeing a move to q0 and on seeing epsilon stack is emptied and hence it is accepted.
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We cannot accept it, there is no transition with input A and top of stack as Zo
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Oh yeah didn't notice that.In that case answer should be D.
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cannot 'aa' accepted with these two transition

$\delta \left ( q_{0},a,X \right )=\left \{ q_{1},X \right \}$

$\delta \left ( q_{1},a,Z_{0} \right )=\left \{ q_{0},Z_{0} \right \}$

Why cannot it accepted?

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But we need to X as top of the stack for this  @Srestha
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I havenot got u

Plz tell more

X is pushing in stack

So, while popping with 'a' , why it is not on top on stack?
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Ma'am for this transition δ(q0,a,X)={q1,X} we need X at top of stack but for string aa when we see first a we have z0 at top of stack and no move is defined for a when top of stack is z0 hence this transition is not possible.
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oh yes

a cannot starting of a string

right?
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Yes ma'am.If n>=1 was there then option A would be correct but in this case answer should be D.
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thanks

this question ditto https://gateoverflow.in/276637/pda-doubt