User:CognitiveMMA/sandbox/GCI4WebSci2022/dsmdeployment

Domain Specific Modeling Tool Deployment

It is hypothesized that defining functional state spaces can lead to an exponential increase in the deployment of domain specific modeling and domain specific modeling tools.

Figure 1: Every path in functional state space is an operation that can potentially be represented in a domain specific modeling tool.

Assume that all functionality of a system in a given domain of its behavior can be understood in terms of N functional states. The number of all possible behaviors of the system within that domain are defined by all the possible paths between those N states. Since each state can potentially transition to N-1 other states, then there are N(N-1) direct or first order transitions. Assuming that a transition does not end up at the same state at which it began, there are N(N-1)(N-2) second order transitions. Assuming that the maximum order of behavior is M, then represent the total number of possible behaviors up to order M for a system that has N functional states as the total T.

From Stirling’s approximation, this number can be exponentially greater than N. Currently, any domain specific modeling tool can be used to represent some subset of behavior of a system within a given domain, but how do the number of those domain specific models and the number of opportunities to deploy those models compare to the number of opportunities to deploy domain specific modeling that might be created in the future through the functional state space approach? For simplicity, assume that on average each domain specific model contains a subset of behaviors with quantity X, and assume that there are Y models. Then if there are Z applications for domain specific modeling, there might be as few as 1 opportunity to deploy a domain specific modeling tool if all those models overlap (all the models describe the same subset of behavior but perhaps in terms of a different set of functions so that each model competes with each other). This involves modeling X operations once. On the other hand, if every model describes behavior that only overlaps moderately, there might be as many as T/Y possible opportunities to deploy domain specific modeling (or an actual number of opportunities limited by Z), each of which involves modeling X operations. However, as the number of domains increases avoiding overlap while developing the models independently becomes increasingly difficult. Furthermore, as the number of operations being modeled grows, making use of those models becomes increasingly difficult as well.

If there is no overlap whatsoever (all behavior is modeled as being part of a contiguous functional state space), there might be as many as T possible operations that might be represented using domain specific modeling. Furthermore the search of operations by ontology permitted by initial approximations of a General Collective Intelligence is predicted to make a far larger number of operations manageable, and the eventual semantic search predicted to be made possible by a true General Collective Intelligence has the potential to make even an exponentially greater number of operations manageable. In addition, collective development orchestrated by a General Collective Intelligence is predicted to exponentially increase the functional state space, and therefore to increase the number of applications Z. Under Stirling’s approximation, this increase in the number of potential applications of domain specific modeling is also expected to be exponential.