## 3 Results
### Pairing T3 SD with DEVS  
In this section, we provide the case for merging the T3 SD framework with the DEVS formalism. To do this, we must first acknowledge some limitations of the current formalism of the T3 SD framework within the context of modern SE.  
The first is that T3 SD is discrete and deterministic modeling. While all systems can be modeled as discrete systems, the margin of error may increase to the point of becoming a useless representation of the real system [10]. Additionally, modeling SE aspects such as the \"ilities\" (e.g., reliability and availability) and risk, in need of theoretical foundations for SE [17], requires the adoption of stochastic, probabilistic models. While [PERSON]'s original Mathematical Theory of SE was based on differential equations [11]; he had been working to add continuous systems to his MBSE framework [21] and recognized the need for event-based system specification [personal communication between [PERSON] and [PERSON], co-author in this paper]. Unfortunately, such research was left unfinished. Therefore, to modernize T3 SD in this area, formalism must be added such as to enable continuous, probabilistic, and discrete event modeling.  
The second is a potential limitation in T3 SD admitted by [PERSON]. The explicit use of [PERSON]'s _system coupling recipe_ (SCR) may have some limits; \"in the SCR where the components in [the vector of systems to be coupled] are not discrete, the coupling function may not exist\" [20]. Therefore, we suggest that for T3 SD to be modernized, the concept of coupling must be further explored.  
The third is that of simulation. It is not unfounded that [PERSON]'s T3 SD be paired with simulation. [PERSON]'s use of system coupling has been credited for providing the system theoretic foundations for modeling and simulation [44]. Although this was in reference to [PERSON]'s first book on the Mathematical Theory of SE [11], simulation of the Moore-based state machines of T3 SD is straight forward. Furthermore, [PERSON] acknowledged the necessity of a minimal system model in his article on reuse of commercial-off-the-shelf (COTS) parts, which \"will make is easier to prove equivalence and therefore facilitate  
Figure 12: Morphisms between big and small systems [10]. Visual representation of the formal mapping of abstraction from the big system to the small system (**a**) and elaboration of the small system to the big system (**b**).  
reuse\" [37]. The concept of a minimal system model is foundational to the Theory of Modeling and Simulation [41]. Additionally, some initial capability of modeling and simulation support for T3 SD was provided in Chapter 12 of [45]. Furthermore, simulation based on [PERSON]'s Mathematical Theory of SE [11] was formalized as the _General Systems Theory_ (_GEST_) Simulator in [46] and later implemented in [47]. The modelling world view of GEST is based on the axiomatic system theory of [PERSON] [11; 48]. GEST is a model and simulation specification language, therefore a GEST program is highly descriptive and acts as a documentation (for communication among humans) as well as a specification (for man-machine communication) [47]. This provides further evidence toward justification of convergence of [PERSON]'s T3 SD with simulation.  
As stated previously, the modernization needs of T3 SD include formalisms beyond discrete and deterministic, further exploration of system coupling, and addition of simulation capability. DEVS provides all of these. The following sections show the relationships between T3 SD and DEVS.