The Entities of Gene Expression Programming - Gene Expression Programming - page 42

2.2.2 Posttranslational Interactions and Linking Functions

We have already seen that translation results in the formation of sub-ETs
with different sizes and shapes, and that the complete expression of the ge-
netic information requires the interaction of these sub-ETs with one another.
Only then will the individual be fully expressed. A very common and useful
strategy consists in the linking of sub-ETs by a particular linking function.
Indeed, most mathematical and Boolean applications are problems of just
one output and, therefore, can benefit from this strategy, in which more com-
plex programs are designed by linking together smaller sub-programs.
When the sub-ETs are algebraic expressions or Boolean expressions, any
mathematical or Boolean function with more than one argument can be used
to link the sub-ETs in a final, multi-subunit ET. For algebraic expressions,
the most frequently chosen functions to link the sub-ETs are addition, sub-
traction, multiplication, or division. For Boolean expressions, the most fre-
quently chosen linking functions are all the interesting functions of two ar-
guments (functions 1, 2, 4, 6, 7, 8, 9, 11, 13, and 14, or, more intelligibly,
NOR, LT, GT, XOR, NAND, AND, NXOR, LOE, GOE, and OR, respec-
tively), or functions of three arguments such as the already familiar IF func-
tion (if a = 1, then b ; else c ) or the 3-multiplexer (also easily described as an
IF THEN ELSE statement: if a = 0, then b ; else c , which, as you can see, is
very similar to the IF function).
However, the linking of sub-ETs with functions of two arguments is much
simpler, as any number of sub-ETs can be linked together one after the other
(see Figure 2.5). On the other hand, the linking of sub-ETs with linking func-
tions of more than two arguments, say n arguments, is more problematic as it
requires n n sub-ETs for a correct linking (see Figure 2.6). Let's now make
this clearer with two examples.
For instance, consider the following chromosome, encoding three alge-
braic sub-ETs linked by addition (the tails are shown in bold):

012345678901201234567890120123456789012
QaQ+-Q bbaaaba +Q+ab+ abababa *-**b+ aabbaba

(2.13)

As you can see in Figure 2.5, the sub-ETs are linked together one after the
other in an orderly fashion. Note that the multi-subunit ET encoded in chro-
mosome (2.13) could be linearly encoded as the following K-expression:

01234567890123456789012
++*Q+-*aQ+*b+aab+abbaab

(2.14)