Minimal Mealy Machines

Minimizing number of states in Mealy machines

We can minimize the number of states in a Mealy machine just as we did for DFAs. The machine below, which prints a $1$ for each $b$ and a $1$ for every other $a$, starting with the first, has one more state than it needs.

Since we want the first $a$ to emit a $1$ and then alternate from there, we can eliminate state $q_0$ and make $q_2$ the initial state.

No move is needed for $b$ ...