# Development Cycle Modeling: Process Risk
## 5 Results
### Examples  
The ADT Information Axiom states that a development project's information content is at its maximum value when the project is least well understood. Conversely, the project's information content reaches its minimum value when the project is most precisely defined, i.e., when it achieves the DEP. Figure 4 shows that the SAbMDE DSpace structure inherently handles development information as required by the ADT Information Axiom. The foundation laid in this paper's previous sections supports a mechanism for effective DSpace navigation and traversal. The mechanism can be demonstrated with simple examples. Begin by defining a DSpace for which Figure 2 is an excerpt. Define the composable elements as follows:  
\[V =\{-,X,+,O\} \tag{20}\] \[R =\{\text{ ``select'' }\} \tag{21}\]  
Note that SAbMDE is domain-independent, so the names and meanings of the composable elements are flexible; they can be whatever is required for the particular domain under development. In this case, the domain is represented by four arbitrary symbols and the ability to select those symbols in sequence. Figure 5 is a tabular representation of the example DSpace.  
Let the DEPs of this DSpace be specified sequences of symbols. An agent can traverse this DSpace with the confidence of reaching the DEPs by applying tests such as (22)-(24) and (26) below, each constructed according to (17).  
\[t_{0} =\left[node(l_{c}+1,k)=\text{designated vocabulary item, }v_{j}= X\right] \tag{22}\] \[t_{1} =\left[node(l_{c}+1,k)=node(l_{c},k_{c})\text{ for }k=1,2,...,Q\right]\] (23) \[t_{2} =\left\{\begin{array}{ll}t_{0}&\text{for }\ \ l=0\\ t_{1}&\text{for }\ \ 1\leq l\leq l_{c}\end{array}\right.\] (24) \[\
u(l,k) =\frac{1}{3}(t_{0}+t_{1}+t_{2}) \tag{25}\]  
For the first example, define a test set, \(T_{0}\), with members (22)-(24). \(T_{0}\) defines a DEP as a contiguous sequence of a specified member of \(V\), in this case, X. Table 2 lays out the traversal mechanism using \(T_{0}\) and (25) applied to the example DSpace. For this simplified example, the DEPDPath stands out as the darkest highlighted X cells in Figure 5 and the low points in Figure 6. The stark distinction of the single DPath is a consequence of the (22) test's specificity. Equation (22) selects DNodes with 100% certainty, it is known at the first composition, and it applies to every subsequent composition.  
Figure 5: A DSpace in tabular format with highlighted DPaths.  
Figure 6: DPath Information for a DSpace traversal using Test Set 0.  
For the second example, include the more ambiguous test (26) in the test set \(T_{1}\) along with (23) and (24). This test set identifies \"cross-like\" vocabulary items for inclusion in a DEP sequence. SAbMDE hypothesizes that the traversal mechanism can rank alternative DPaths and, thus, guide an agent to the best DEP.  
\[t_{4} =\left[node(l_{c}+1,k)=\text{cross-like, }\tau_{4}=\left\{ \begin{array}{ccc}0.0&\text{for}&-\\ 1.0&\text{for}&\text{X}\\ 0.5&\text{for}&+\\ 0.0&\text{for}&\text{O}\end{array}\right\}\right. \tag{26}\] \[\
u(l,k) =\frac{1}{3}(t_{4}+t_{1}+t_{2}) \tag{27}\]  
Application of test set \(T_{1}\) and (27) identifies the 16 DPaths highlighted in Figure 5. Table 3 shows the states of the traversal mechanism, at each composition index, as it drives those DPaths toward their corresponding DEPs. Table 4 also shows the test results, the DNode probabilities, and the information for each DPath. Figure 7 is a graphical representation of Table 4. As hypothesized, the relative information values distinguish the DPaths from one another. At any composition level, an agent can compute the likelihood that the current DPath is the best one. Or, to the degree that the agent projects the DPaths forward (as has been done here), the agent can get a sense of the best DPath options.  
Figure 7: DPath Information for a DSpace traversal using Test Set 1.