## 3 Results
### A Systematic Description of the T3 SD Metamodel
#### 3.1.5 Illustration of T3 SD Concepts
Consider now two CR such that lower development cost is preferred over higher development cost. These requirements set an order on the space of BSDs such that BSD\({}_{1}\) > BSD\({}_{2}\) > BSD\({}_{4}\) > BSD\({}_{3}\) > BSD\({}_{5}\), where > denotes preferred to. The corresponding illustration of the buildability perspective of an engineered flashlight is shown in Figure 9.  
Continuing with the flashlight example, we find the intersection of the space of FSD and the space of BSD by evaluating the functionality of the systems in the space of BSDs and buildability of the systems in the space of FSDs. These are shown in Figure 10, where each pair block diagram/state machine represent one possible solution inside or outside of the implementability space. **For real-world application, a homomorphism is a mapping from a subset of the cross-product of the components states of BSD to the target system (FSD) where the subset can be shown to be a subsystem (i.e., closed under state transitions). For simplification of this illustration, we show only a representation of the homomorphic mapping of the resultant (Z@) of the BSD to the FSD. ** It can be seen that BSD\({}_{1}\), BSD\({}_{2}\), and BSD\({}_{3}\) do not present any mode of behavior that is homomorphic to solutions in the space of FSD, since the inputs of BSD\({}_{1}\) and BSD\({}_{3}\) and the outputs of the three of them are different from those required by the IOR. Therefore, BSD\({}_{1}\) and BSD\({}_{2}\) do not belong to the space of ISDs. Similarly, it can also be seen that FSD\({}_{2}\) does not have a corresponding BSD. Therefore, FSD\({}_{2}\) does not belong to the space of ISDs. Figure 9: Practical illustration of the Buildability perspective to showcase the process for engineering a flashlight; including system designs that are built from available technology and an ordering according to preferred cost. The diagram does not represent a single model of the system, but a solution space. Each pair state machine/block diagram represents one possible solution inside the buildability space. This figure is used only to support our narrative to explain [PERSON]’s T3 SD. The figure is NOT a formal visualization of any model. The functionality of BSD\({}_{4}\) is, however, directly mappable to FSD\({}_{1}\), and hence BSD\({}_{4}\) belongs to the space of ISDs; and we denote it by ISD\({}_{1}\). BSD\({}_{5}\) has a mode of behavior that is mappable to FSD\({}_{1}\) (when P\({}_{\text{on2}}\) is unused) and a mode of behavior that is mappable to FSD\({}_{3}\) (when P\({}_{\text{on1}}\) is unused). Both solutions belong to the space of ISDs and we denote them by ISD\({}_{2}\) and ISD\({}_{3}\), respectively. Furthermore, because no solution in the BSD implements a mode of operation that is homomorphic to the behavior of FSD\({}_{2}\), FSD\({}_{2}\) stays outside of the space of ISDs. Consider now TR that (simplistically stated) lower cost takes precedence over higher light. (A detailed description of different types of TR can be found in [40].) This requirement sets an order on the space of ISDs such that ISD\({}_{1}\) > ISD\({}_{2}\) = ISD\({}_{3}\), where > denotes preferred to and = denotes indifference. The corresponding illustration of the implementability perspective of an engineered flashlight is shown in Figure 10.