A Mealy machine is a particular type of finite state automaton.
A Mealy machine with input alphabet $A$ and output alphabet, $B$ is just a deterministic finite automaton?,which produces a letter of the output alphabet, $B$ at every transition step. More formally
A finite Mealy machine, $\mathbf{A}$, consists of
$Q$, a finite set of states;
$A$, an input alphabet;
$B$, an output alphabet;
$q_0$, an initial state;
$\delta: Q\times A\to Q$, a transition function;
and
Again as for Moore machines, there is an output response function $\omega_\mathbf{A}:A^*\to B^*$ defined s follows:
if $x= x_1 \ldots x_n\in A^*$ and the states that $\mathbf{A}$ passes through when processing this string are $q_0, q_1, \ldots, q_n$, so diagrammatically
define $\omega_\mathbf{A}(x)= \lambda(q_0,x_1)\ldots \lambda(q_{n-1},x_n)$.
Mealy machines and Moore machines have essentially the same descriptive power.
Mark V. Lawson, Finite automata, CRC Press, see also here for a shorter version in the form of Course Notes.
Dirk Pattinson, An Introduction to the Theory of Coalgebras, here.
Last revised on July 18, 2019 at 09:57:09. See the history of this page for a list of all contributions to it.