## 3 Results
### A Systematic Description of the T3 SD Metamodel
#### 3.1.5 Illustration of T3 SD Concepts  
For the practical illustration of the flashlight, let us consider a set of system requirements such that the system must provide at least certain level of light when receiving a dedicated command, \(P_{\text{on}}\), to do so and must provide no light when receiving another dedicated command, \(P_{\text{off}}\). We denote the no light condition and the minimum level of light by \(L_{0}\) and \(L_{>2}\), respectively. Furthermore, we define \(L_{0}\) and \(L_{>2}\) to be mutually exclusive, as are the pair \(P_{\text{off}}\) and \(P_{\text{on}}\). The IOR define that, when \(P_{\text{on}}\), the system provides \(L_{>1}\), and when \(P_{\text{off}}\), the system provides \(L_{0}\). Furthermore, \(L_{0}\) and \(L_{>1}\) are defined as different values of a single output port and \(P_{\text{off}}\) and \(P_{\text{on}}\) as different values of a single input port. The IOR defines the space of FSDs shown in Figure 8, where each state machine represents one possible solution in the functionality space. [PERSON] selected the Moore state machine [38] as the basis for the FSDs. For simplicity, we have considered six different FSD's, denoted by FSDi, with \(i=1,\,\ldots\,.6\). \(L_{3}\) denotes a level of light intensity higher than \(L_{2}\), \(L_{0}\) denotes a level of light intensity lower than \(L_{1}\) but higher than no light, \(L_{5}\) denotes an intermittent light, and \(P\) denotes a single type of command. FSDi, FSDi, and FSDi meet the IOR and hence belong to the space of FSD, whereas FSDi, FSDi, and FSDi do not meet the IOR and hence do not belong to the space of FSD defined by IOR. Consider now two PR, such that more light intensity is preferred to less, and uniform lighting is preferred to non-uniform lighting, and the latter is preferred over the former. These requirements set an order on the space of FSDs such that \(FSD_{3}\succ FSD_{2}\succ FSD_{1}\). The corresponding illustration of the functional perspective of an engineered flashlight is shown in Figure 8.  
Continuing with the flashlight example, let us consider a set of TYR such that the available technologies include three different light sources (denoted by \(Z_{1}\), \(Z_{2}\), and \(Z_{3}\), providing intensity levels \(L_{1}\), \(L_{2}\), and \(L_{3}\), respectively), one sounding alarm (denoted by \(Z_{4}\)), and two control systems (denoted by \(Z_{5}\), \(Z_{6}\), and \(Z_{7}\), providing one, two, and three input values, respectively). These TYR give form to a space of BSDs formed by any meaningful combination of \(Z_{1},\ldots,Z_{7}\). For simplicity, we only show five of such BSDs, which we denote by BSDi, with \(i=1,\,\ldots\,.5\), and depict in Figure 8, where each pair of box with internal blocks and state machine represent one solution in the buildability space. While those solutions present behaviors, note that these are irrelevant in the buildability space and only TYR are considered. This is why BSD3, representing a sound alarm, is considered an  
Figure 8: Practical illustration of the T3 SD Functionality perspective to showcase the process for engineering a flashlight; including system designs that meet the required input/output, system designs that do not meet the required input/output, and an ordering according to preferred performance. The diagram does not represent a single model of the system, but a solution space. Each state machine represents one possible solution inside or outside of the functionality 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. acceptable solution. Furthermore, in a **real-world application, the state space of a coupled model is the cross-product of the state sets of the components. Rather than show the state space, we show the minimization of the result (Z@) of each BSD for simplification of this illustration. The minimization of a system is its homomorphic image with the least number of states**[37].