I am studying PDA at the moment, and I came up with this question.
The figure above tells me that although both PDA accept the same language, one is non-deterministic and the other is deterministic. I don't understand the reason why the first one in non-deterministic. As far as I know, the conditions for DPDA is that
1) every transition should have at most one move
2) if $\delta$(q,a,X) is not empty, then $\delta$(q,$\epsilon$,X) should be empty.
However, since the first PDA does satisfy the above conditions therefore I thought it is DPDA.
What am I missing?
Thanks in advance.