Constructing the Environment for zcs

First we will provide an environment according to the description as given in 4.4. This is a scilab programm called 'environment.sce' and it contains several functions. One is called [GRID]=gridgen(Y,X). This function generates from the two numbers Y and X a two-dimensional grid according to the structure of a wood1-world. In the theory such a function is not necessary because we simply assume some environment $E$ as 'given'.

Realizing an environment in the computer induces another problem. If we have more than one agent active in the same environment using a sequential processing we have to define some 'protocol' how we 'simulate' simultaneous actions. The most simple approach is to make before any new action cycle a random ordering and then process every agent one after the other.

To realize this we have to assume that the simulated environment $E^{S}$ embraces at least two components: (i) a two-dimensional grid $G$ for the 'space' of the environment and (ii) a list of registered agents $AL$ with the basic information agent identifier, position, direction, new action, and reward $\langle AID, POS, DIR, ACT, REW\rangle$. Based on these informations it is possible to compute the content of visual input as well as the possible next moves. Thus we will have

$$EF^{S}(x) iff x = \langle E^{S}, A, \iota, \mu\rangle$$ (4.51)

$$E^{S} = \langle G, AL\rangle$$ (4.52)

$$G = (2^{POS \times OBJ})^{n,m}$$ (4.53)

$$POS = Y \times X$$ (4.54)

$$OBJ \in \{'O', 'F', '.', 'A_{i}'\}$$ (4.55)

$$AL \in (AID \times POS \times DIR \times ACT \times REW)^{n}$$ (4.56)

$$A = Agents$$ (4.57)

$$\iota : E^{S} \leftrightarrow A^{n}$$ (4.58)

$$\mu : E^{S} \times \iota \times A^{n} \longmapsto LOG^{n}$$ (4.59)

$$A(x) iff x = \langle AB, \gamma\rangle$$ (4.60)

Where the objects $\{'O', 'F', '.', 'A_{i}'\}$ represent the possible objects which can placed in one position of the grid.