Mealy · Rational transduction
Serial binary adder
Adds two arbitrarily long binary numbers with just two states: feed bit-pairs LSB-first, read the sum off the output. Carry in the state, nothing else — the circuit in your CPU.
The author’s examples, run
01 11 10 00 → reject · 100111 11 00 → reject · 01110 10 → reject · 11