Hello,
the very definitions of both automata do not differ much from each other, although they are quite lengthy.
Mealy's (finite) automaton is by definition an ordered "five":
M =
wherein:
X = {x1, ..., xn} - a set of input letters (signals) (input alphabet),
S = {s1, ..., sn} - a set of internal states (internal alphabet),
Y = {y1, ..., yn} - set of output letters (signals) (output alphabet),
these sets are finite and non-empty.
?: D? -> S - transition function (transient)
?: D? -> Y - output function (output)
Whereas:
D? - transition function domain,
D? - the domain of output functions.
The transition function assigns each pair consisting of the input letter and the current state and belonging to D? - next state.
The function of outputs assigns each pair of the initial letter and the current state and belonging to D? - the initial letter.
A Moore-type (finite) automaton is defined from the definition of a Mealy (finite) automaton for which there is a specific condition:
D? is contained in S (the domain of the function of outputs in the set of internal states).
The given definitions show that in the case of a Mealy automaton, the initial letters are associated with changes of states - with transitions, and in the case of a Moore automaton - with states.
There is a close relationship between Mealy-type automata and Moore-type automata: having a given automaton of one type, one can always give an automaton of the other type, equivalent to it in a certain sense.
Regards