Formal description of PDA

Question

I remember how to do a formal description of an FSM, but doing one for a PDA looks a little different. Can anyone help explain the circled part? I normally take good notes, but can't seem to find anything on this in my notebook or anywhere else. Any help is appreciated.

Answer 1

They are your transitions as the diagram shows. Have a look here.

Answer 2

While working for push down automaton we have two types: Graphical and Instantaneous.
In graphical PDA, we show the stack operations diagrammatically.
In instantaneous PDA, we use instantaneous rules.
Your circled part belongs to the later category.
These are the rules which mean the following:
Before starting, Be clear about that initially stack has an epsilon value. And for every push there can be a corresponding pop operation.
So in the first line i.e, ((S,a,E),(S,a)) -> When the first alphabet a will be entered the state will remain the same and output will be a. Also, as long as input is a state will remain the same.
In the second line ((S,b,a),(f,E)) -> This rule states that when after a you have b alphabet as input the state will now change, a will be popped out and any other alphabet rather than S can be used to show the state of change and the value will be epsilon now.
In the last line, it is depicted that as the input is b again, state has remained the same.