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Suppose th $PDA, $    $P=(\{q,p\},\{0,1\},\{Z_{0},X\},\delta,q,Z_{0}.\{p\})$ has the following transition function$:$

  1. $\delta(q,0,Z_{0})=\{(q,XZ_{0})\}$
  2. $\delta(q,0,X)=\{(q,XX)\}$
  3. $\delta(q,1,X)=\{(q,X)\}$
  4. $\delta(q,\in,X)=\{p,\in\}$
  5. $\delta(p,\in,X)=\{p,\in\}$
  6. $\delta(p,1,X)=\{(p,XX)\}$
  7. $\delta(p,1,Z_{0})=\{p,\in\}$

Starting from the initial $ID$ $(q,w,Z_{0}),$

  1. Convert $P$ to another $PDA$  $P_{1}$ that accepts by empty stack the same language that $P$ accepts by final state;i.e.,$N(P_{1})=L(P).$
  2.  Find a $PDA$  $P_{2}$ such that $L(P_{2})=N(P)$ i.e., $P_{2}$ accepts by final state what $P$ accepts by empty stack.

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