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Consider the Context free language  which has equal no of as and bs. 

eg- abab

Since a proper prefix ab also belongs to this language, this language does not satisfy prefix property as far as i understand. 

But we can clearly draw a deterministic PDA with empty stack acceptance for it.

My doubt is that we cannot make DPDA with empty stack for CFL without prefix property. 

But above example forms a contradiction. Please resolve my doubt. I am getting confused.

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