# Formal definition of an empty stack accepting PDA

PDA's are usually defined using the 7-tuple convention.

$$M=(Q, \Sigma, \Gamma, \delta, q_{0}, Z, F)$$

F is the set of accepting states.

I want to design a PDA accepting by empty stack, so using this notation makes no sense, as I don't need F and I want to make the acceptance condition clear.

How is this usually done? Can I just dismiss F?

$$M'=(Q, \Sigma, \Gamma, \delta, q_{0}, Z)$$

When the stack is finished you can go to the specified state which shows the empty stack. In addition, when you reach in a state which you found it's a solution but the stack is not empty, iterate over a "pop" action to empty the stack and finally go the empty stack state.

Hence, you can explain this PD using the defined notation.

• I know that empty stack and final state PDA's have the same expressive power. Yet I want to write down one automaton accepting by empty stack. E.g.: How could you formally write down an automaton for the Grammer with one production: S->a which accepts by empty stack? – PascalIv Jan 9 at 12:17