2DFT · Regular transduction (two-way)
Copy twice: w ↦ ww
Sweeps the input printing it, rewinds, then sweeps and prints again — doubling the word. The canonical transduction that separates two-way transducers from one-way ones.
The author’s examples, run
ab → accept · ababa → accept · aaabb → accept · abbabbba → accept · babaaabb → accept · aabbaabb