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FIGURE 5. Circuitry and basic components of a recursive function computer. F com-
puting element; X input proper; Y¢, recursive input of a previous output Y¢ D, delay;
T, translates action Y into a representation of Y acceptable to F.
or, more conveniently, if we drop the reference to t by merely writing Y and
X, and for the previous state Y¢ and X¢:
(
)
.
Y
=
F X, Y
¢
However, this does not yet tell us the actual output of the system,
because we do not know the value of one of its inputs, namely Y¢, i.e., its
previous output. But this can be determined, using the recursive definition
of Y:
(
)
YFX, Y
¢=
¢ ¢¢
or in words: the previous output is a function of the previous input and its
previous-previous output. Hence, by inserting the expression for Y¢ into the
earlier equation for Y, the present output becomes:
(
)
.
Y
=
F X, X , Y
¢
¢¢
Again we may ask for the value of the previous-previous output, and by
applying again the recursion, we will arrive at an expression which leads us
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