PDT · Pushdown transduction
Classic: aⁿbⁿ ↦ bⁿaⁿ
Accepts aⁿbⁿ with the stack while printing b for every a and a for every b — so the output is bⁿaⁿ. Recognition and transduction in one machine.
The author’s examples, run
ab → accept · baaabb → accept · bbaaaaabbb → accept · bbbaaaaab → rejectabb → reject