## 3 Results
### A Brief Review of DEVS and Associated Formalism
#### 3.2.2 Hierarchy of System Specifications and Associated Morphisms
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Level** & **Specification Name** & **What We Know at This Level** & **Example: An Engineered Flashlight System** \\ \hline
**0** & I/O Frame & How to stimulate the system with inputs; what variables to measure and how to observe them over a time base; & The flashlight has inputs and outputs at external black-box level, input set of symbols representing pressing on (Pon) and pressing off (Poff); and the output set of symbols for light intensity (L2 and L0). \\ \hline
**1** & I/O Relation & Time-indexed data collected from a source system; consists of input/output pairs & For each input that the flashlight recognizes, the set of possible outputs that the flashlight can produce \\ \hline
**2** & I/O Function & Knowledge of initial state; given an initial state, every input stimulus produces a unique output. & Assuming knowledge of the flashlight’s initial state at the onset of its operational lifecycle, the unique output time segment response to each input time segment. \\ \hline
**3** & I/O System & How states are affected by inputs; given a state and an input what is the state after the input stimulus is over; what output event is generated by a state. & How the flashlight transits from state to state under input signals and generates output signals from the current state \\ \hline
**4** & Structured System & The I/O System state is described in terms of a cross-product of state sets, such as a point in a vector space. & The description of the flashlight transits from state to state under input signals in terms of a point in a real valued vector space as in a linear state-based system. \\ \hline
**5** & Multi-component & The system is specified as composition of components whose outputs are directly linked to inputs of other components & A description of a flashlight’s I/O behavior in terms of components and their direct interaction in the manner of a cellular automaton (Game of Life). \\ \hline
**6** & Network of Systems & Components and how they are coupled together. The components can be specified at lower levels or can even be structure systems themselves—leading to hierarchical structure. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Informal Description of the Levels of System Specification. basic levels of system specification forming a Systems Specification Hierarchy with arrows directing their associated morphisms. At each level we can know, or can specify, important things about a system that are not knowable, or specifiable, at lower levels. Based on the arrangement of system levels shown in Figure 11, we distinguish between vertical and horizontal relations. A horizontal relation is called an association mapping. It takes a system at one level of specification and elaborates it or abstracts it at another level of specification. The motion in the direction from Level 6 (Network of Systems) to Level 0 (I/O Frame) formally represents the process by which a simulator generates the behavior of a model. While the vertical association of specifications is straightforward, the association in the horizontal direction from Level 0 (I/O Frame) to Level 6 (Network of Systems) is much less so because travel in this direction requires acquisition or specification of additional system knowledge. In other words, it is possible that many structures exhibit the same behavior. Thus, recovering a unique structure from a given behavior is not possible except in special circumstances, called justifying conditions. For a complete description of the justifying conditions enabling structural inference, see [41]. The general concepts of _homomorphism and isomorphism_ relate to the vertical relations which relate system models at the same level of specification. Corresponding to each of the various levels at which a system may be known, described, or specified, is a relation appropriate to a pair of systems specified at that level.