Editing Gene expression programming (section)

==Expression trees: the phenotype==
As shown [[gene expression programming#Encoding: the genotype|above]], the genes of gene expression programming have all the same size. However, these fixed length strings code for [[expression tree]]s of different sizes. This means that the size of the coding regions varies from gene to gene, allowing for adaptation and evolution to occur smoothly.

For example, the mathematical expression:
:<math>\sqrt{(a-b)(c+d)} \, </math>
can also be represented as an [[expression tree]]:

{| align="center" border="0" cellpadding="4" cellspacing="0"
| [[File:GEP expression tree, k-expression Q*-+abcd.png]]
|}

where "Q” represents the square root function.

This kind of expression tree consists of the phenotypic expression of GEP genes, whereas the genes are linear strings encoding these complex structures. For this particular example, the linear string corresponds to:

:<code><nowiki>01234567</nowiki></code>
:
:<code><nowiki>Q*-+abcd</nowiki></code>

which is the straightforward reading of the expression tree from top to bottom and from left to right. These linear strings are called k-expressions (from [[Karva notation]]).

Going from k-expressions to expression trees is also very simple. For example, the following k-expression:

:<code><nowiki>01234567890</nowiki></code>
:
:<code><nowiki>Q*b**+baQba</nowiki></code>

is composed of two different terminals (the variables “a” and “b”), two different functions of two arguments (“*” and “+”), and a function of one argument (“Q”). Its expression gives:

{| align="center" border="0" cellpadding="4" cellspacing="0"
| [[File:GEP expression tree, k-expression Q*b**+baQba.png]]
|}