There are two ways to define the language of a PDA ( ). because there are two notions of acceptance:
In our example the PDA would accept because and . Hence we conclude .
On the other hand since there is no successful sequence of IDs starting with we know that .
If we specify a PDA for acceptance by empty stack we will leave out the set of final states and just use .
Our example automaton also works if we leave out and use acceptance by empty stack.
We can always turn a PDA which use one acceptance method into one which uses the other. Hence, both acceptance criteria specify the same class of languages.