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section 3.2.3 (number of hits, hits with penalty, sensitivity/specificity, and positive
predictive value/negative predictive value fitness functions) and then comple-
ment them with a parsimony term.
Consider, for instance, the number of hits fitness function evaluated by
equation (3.8). In this case, the raw fitness
rf
i
of an individual program
i
corresponds to the number of hits and, therefore, raw maximum fitness
rf
max
consists of the total number of fitness cases. And the overall fitness
f
i
(or
fitness with parsimony pressure) is evaluated by the formula:
§
·
1
S
S
f
rf
¨
©
1
max
i
¸
¹
(4.21)
i
i
5000
S
S
max
min
where
S
i
is the size of the program,
S
max
and
S
min
represent, respectively, maxi-
mum and minimum program sizes and are evaluated by the formulas:
S
max
=
G
(
h
+
t
) (4.22)
S
min
=
G
(4.23)
where
G
is the number of genes, and
h
and
t
are the head and tail sizes (note
that, for simplicity, the linking function was not taken into account). Thus,
when
rf
i
=
rf
max
and
S
i
=
S
min
(highly improbable, though, as this can only
happen for very simple functions as this means that all the sub-ETs are com-
posed of just one node),
f
i
=
f
max
, with
f
max
evaluated by the formula:
f
1
0002
rf
(4.24)
max
max
4.3.2 Universal Logical Systems
In logic there are quite a few widely studied and commonly used universal
systems that have been used to design a wide range of logical functions or
circuits. Why one is chosen and not another is most of the times a matter of
efficiency, which mostly depends on the compactness of the solutions one
can design with it.
By definition, a universal logical system is any set of logical functions
that can be used to describe any other logical function. The most famous is
the classical Boolean system of {NOT, AND, OR}, an extremely convenient
system because we also think in terms of ANDs, ORs, and NOTs. But, in
truth, this system is quite redundant, for it is possible to describe any logical
function using just NOTs and ANDs or NOTs and ORs. So, if one creates a
