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I'm confuse about the correctness of this State Diagram.

this part is anbn so it can't be regular .

now i am either unable to get the lower part or its incorrect.

its accepting Null clearly now if our string an then it will push a to stack now i don't know how can there be a possible transition for state 0 (lower) as stack element is a that's not Null but from initial state , state 0(lower) transition only possible when stack contain Null , which is clearly not possible, stack content can only be null when there is a direct transition form initial state to state 0 (lower) without consuming a.

tell me if i made some argument wrong.

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