I came across https://en.wikipedia.org/wiki/Automata-based_programming which argues there are significant advantages to writing your program as a FSM (finite automaton). This of course is a well known design pattern with lots of tutorials https://www.youtube.com/watch?v=4Lom_lqSGoY

Is there a similar advantage to writing your program as a Pushdown Automaton (PDA)? Can you give (or link to) an example of a program written as a PDA?

I imagine there is an advantage to restricting your program to something lower down the Chomsky Hierarchy as such programs have lower complexity.