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 that1) every transition should have at most one move2) 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.
Why is this NPDA?
automata;pushdown automata
The first PDA doesn't comply the second condition because $|\delta (q0,a,\epsilon)| = |\delta (q0,\epsilon,\epsilon)| = 1$.