Embedding zcs into the EF-Framwork

There is no direct mapping from $zcs$ into the $EF$ framework because Wilson does not offer a complete structural definition of the $zcs$. Instead he presents a diagram Fig.1 on page 2 of his paper [347] and in the accompanying text he explains the different components of the diagram in an informal way. To explain our embedding we have to show here a copy of his diagram with additional markings added from the author of this text.

Figure 4.5: Structural comparison between zcs and EF framework

Figure 4.5 shows that all the main components of the $EF$ framework can be identified in the drawing of Wilson.

1. Environment: Wilson assumes an environment $E$ which is the source of binary strings encoding the sensory inputs for the zcs. These binary encodings are the result of a translation process from certain kinds of 'objects' in his wood1-world (for a more detailed description of this translation process see the section 4.4). The environment is also the destination for the actions of the zcs.
2. Interface: Wilson does not explicitly talk about an interface $\iota$ between the environment $E$ and the agent $A$. But he distinguishes detectors -labeled $\Sigma^{*}$ in the $EF$ framework-, which receive input from the environment as well as effectors -labeled $\Xi^{*}$ in the $EF$ environment-, which send action signals to the environment. These assumptions imply some mappings from the environment $E$ to the detectors as well as from the effectors to the environment. Furthermore does Wilson assume explicit rewards from the environment to the agent. In the $EF$ framework these mappings are explicitly named by ainp(), aout(), fit(). They together constitute the interface $\iota$.
3. Agent: The agent according to Wilson is a structure containing some sets including the detector and effector values and some mappings. In the $EF$ framework a general system function $\gamma$ is assumed which maps the input to the output. The details of this system function $\gamma$ are left open for different kinds of differentiations.

Thus while the general structure from zcs maps well to the $EF$ framework are the details of the zcs-system function special. We will reconstruct this function below. For this we work out the theoretical definitions and simultaneously a software version. In some cases we will use the details of the software functions as defining operations for the theoretical mappings as well.