Standard forms of DPDA s

It is possible to put every DPDA in some standard form where the only stack operations are to erase the top symbol without putting anything else on the stack; or to push a single symbol onto the stack on top of the symbol that was previously on top; or to leave the stack unchanged. The following two lemma establishes this fact.

Lemma 1 If L is a DCFL, then L=L(M) for some such that if , than

Proof : Let the accepts L and has a move with The DPDAM simulates this move by using some more states and a sequence of moves as follows.

      Let

      Let are nonaccepting states in M (which is not in M'). The move

       in M' is redefined as in M.