Is there any method or procedure can measure model complexity in term of the model network?
Two directed graphs or networks can represent a model. One graph represents the model's executable representation (e.g., software). The other digraph represents the state space of the behavior that the model's executable representation generates when it executes in a computational environment. The vertices of the state space graph represent all of the states that the model may assume and the arcs represent all of the possible transitions between states that the model can make when its executable representation is executed. In my opinion, and there is by no means consensus on this, the size of a model's state space digraph (i.e., the total number of arcs) provides the most accurate and meaningful measure of model complexity. All of the other measures that people have suggested only approximate this measure (e.g., entropy, cyclomatic complexity). Trouble is ... measuring the size of a model's state space graph is hard and may require executing the model over its entire scope of input to determine. That's why people use other, more approximate but computable, complexity measures.
In the Statecharts framework, components (i.e. parallel Statecharts sections) interact by exchanging triggering events and by having guards whose conditions refer to other components. Considering such mutual dependencies among components may be at the basis of a measure of complexity for the model. The more interdependent are the components of the graphs, the more coupling exists among them. Coupling is a measure of the complexity of the model, since the more coupled are different components, the more difficult becomes to understand, reuse, modify single components. It would be then interesting to base a measure of the complexity on the measure of the mutual coupling among the modules. I am interested in developing such a measure. We have a method (called Part-Whole Statecharts) which allows to obtain the same behaviour of interacting elements by using stand-alone, non interacting elements. The global behaviour is represented by an additional state machine, called "whole". Such a state machine contains the same coordinating information of the mutual references, and as such may be a measure itself of the complexity of the model.
There is no such thing as an absolute measure of complexity of a model. You can (potentially) compare two models, assuming both have been constructed using same modelling paradigm and at the same level of abstraction, based on some suitable complexity metric (e.g., number of nodes in the model network). Even then, the result may depend on choice of modelling paradigm and complexity metric.
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