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my question is as it is odd length palindrome , so  it can be ababa , right ?

Now , in the given diagram , they have not mentioned the scenario :

1)  when a is the stack top element and input symbol is b  ( b , a / ? ) 

2)  when b is the stack top element and input symbol is a ( a, b / ? )

Now , my question is - without these two transitions can we design this pda ? ( as it is done in the given ans )

in Theory of Computation by Active (3.8k points) | 474 views
+1
In the diagram $\epsilon$ is used to show that stack top does not matter for the transition.

1 Answer

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According to me this question is unclear but if we thinks that ∊ represents that at the top of the stack there can be anything then only we can say option c is correct ..

But in gate they will not ask such  unclear and confusing question...

at state B

there should be following transitions specified..

∱(B,b,Zo)=(B,bZ0) , ∱(B,a,Zo)=(B,aZ0) , ∱(B,b,b)=(B,bb), ∱(B,b,a)=(B,ba), 

∱(B,a,a)=(B,aa) , ∱(B,a,b)=(B,ab)  

Hope this will clear your doubt...

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