Moore machine

Remarks

Example: let $\Sigma = \Gamma = \set{0, 1}$, $Q = \set{0, 1}$, $q_0 = 0$, $\delta(q, a) = q + a \bmod 2$ and $\lambda(q) = q$. Then $q_i$ is the parity of the number of $1$'s among $a_1, \ldots, a_i$, and on $0110$ the output is $00100$. Non-example: a machine with output function $\lambda \colon Q \times \Sigma \to \Gamma$, depending on the input symbol too, fails clause 3; it is a Mealy machine. With this convention the output has length $n + 1$; some authors drop $\lambda(q_0)$ so that input and output have the same length. A Moore machine gives a Mealy machine with the same states by setting $\lambda'(q, a) = \lambda(\delta(q, a))$; the converse needs, in general, up to $\abs{Q} \cdot \abs{\Gamma}$ states.