# How do I normalize a push down automaton?

Looking at the above PDA, I am unsure whether or not it is normalized. Specifically, the loop transition from $q_1$ to $q_1$, because I know a transition must either push OR pop from the stack. Does this mean that there must be two separate transitions to push the * and then pop the *? Or is it normalized as is? Is it okay to have multiple transitions from a single state to another, some of which pop, and some of which push?

• I encourage you to edit your question to include a self-contained definition of what you mean by "normalized". If you don't know what the definition is, you might want to ask whoever is using that term with you to define their terms. Thank you! – D.W. Mar 4 '17 at 0:01

For the example you give, a transition is not represented by a directed edge, but by a directed edge together with a label. If you have an edge with two labels, as in your loop on $q_1$, that represents two transitions. Trying to do it with two separate loop edges would only make your diagram less readable.