## 5 Results and Discussion
### Discussion  
The advantage of described here process is that it enables designing the system description adopted in this paper in the form of a table describing the responses of the system without knowing its structure and principles of action. At the same time, it ensures that the designed system will operate exactly as described in the response table. It can be treated as a \"black box\". The main advantage is that to obtain the design of a sequential circuit, all you need is the system response table, which can be obtained by connecting probes to any working system. Thus you can create a functional copy of the system without knowing its internal structure. Therefore, even with relatively simple systems such as those presented here, it can have practical applications. The limitation of the adopted solution is the fact that it is difficult to describe the required reactions of more complex systems. What can be done to obtain a complex description using a table describing the answers of e.g., a simple processor? To fully describe the behavior of a sequential system based solely on descriptions of its input and output states, it would be necessary to account for all possible future scenarios. For continuous operation, this would require an infinite number of rows in the table describing the system, which is obviously impossible. Consequently, we use tables that illustrate only cyclic actions rather than all potential future responses. The difficulties in creating such tables are presented in the examples in Sections 5.1-5.3. Additional issues may arise where a properly functioning system gradually changes its behavior over time. This challenge is highlighted in Section 5.2. The more complex the system, the harder it becomes to describe its behavior solely based on input and output states. This is one of the challenges for further development using M-CGP in the design of sequential systems. Various directions of research can be adopted here, starting with replacing these tables with a completely different description but still requiring that one can be obtained by testing the response of a system treated as a black box. Other such descriptions can also include, for example, tables containing the relevant symbols. Another approach concerns the analysis of the impact the parameters have on the efficacy and efficiency of M-CGP in the design of sequential systems. We can study the influence of parameters here such as \(number\_columnsCGP\), mutation probability, population size, mutation method, selection method, it is also possible to introduce crossbreeding. A totally different path is to use M-CGP to automatically generate neural networks, where we can deal with various types of layers and specific communication between layers of different types. During the experiments, the \(number\_columnCGP\) parameter initially started with a predefined value. If a correctly functioning digital system, as described by the table, was achieved within a given number of generations, the parameter was reduced. This process continued until it was no longer possible to obtain a functioning system. This approach determined the minimal value of the \(number\_columnCGP\) parameter required to produce a digital system that functioned according to the description. However, if no solution was found for the initial \(number\_columnCGP\) parameter value, the parameter was increased until the desired outcome was achieved. The above approach proved superior to using a target function based on the number of elements, which could lead to the system becoming trapped in local minima. At the same time, this solution made it possible to obtain systems without an exceedingly large number of elements. For instance, Figure 5 shows a system generated with \(number\_columnCGP=50\), consisting of 27 elements. In contrast, Figure 3 presents a system executing the same function with \(number\_columnCGP=8\), which consists of only 7 elements. As shown, this comparison highlights the critical impact of this parameter on system design.