Repeating the introductory example in the more general framework we can write
(3.25) | |||
(3.26) | |||
(3.27) | |||
(3.28) | |||
(3.29) | |||
(3.30) | |||
(3.31) | |||
(3.32) |
The structure includes the environment set , which consist only of a feedback (fitness) function of the environment feeding back the effects of the behavior of a phenotype in an environment. In case of there is no real action string (see below). The fitness is computed directly on the basis of the phenotype without action (see below). The fiteness-function is given as (which could easily replaced by any other kind of function ). This environmental fiteness function generates 'fitness' as a fitness-string as a decimal number (which can be encoded as binary string).
The set of phenotypes is a set of decimal numbers which whill be computed out of the genomes by the interpretation (growth-)function , mapping genomes into phenotypes by translating binary strings into decimal numbers (which could be done in different ways).
A system function as part of the phenotype mapping input strings into output strings is not available and therefore also no action-strings of the phenotypes, .
The genetic function is realized by a concatenation of the functions , , and . The fitness feedbacks encoded in the input strings is implicitly given as input of these partial functions.
Gerd Doeben-Henisch 2012-03-31