This PDA accepts by empty stack. The language accepted by this PDA is the set of strings with an equal number of $\text{'}$a$\text{'}$s and $\text{'}$b$\text{'}$s$,$ where each $\text{'}$a$\text{'}$ from the left has a corresponding $\text{'}$b$\text{'}$ from the right, as defined by the given grammar.