## 5 Characteristics of a Tested Object--Station System
Several can be chosen from an entire pool of checks, and their implementation should be sufficient to adequately monitor the state. This rule can be expressed by the relationship: \[ \begin{array}{l}x_{11}+x_{12}+x_{13}+\ldots+x_{1j}\geq 0\\ x_{21}+x_{22}+x_{23}+\ldots+x_{2j}\geq 0\\ x_{31}+x_{32}+x_{33}+\ldots+x_{3j}\geq 0\\ \ldots\\ x_{i1}+x_{i2}+x_{i3}+\ldots+x_{ij}\geq 0\end{array} \] (4) \(x_{ij}\)--coordinates of individual algorithm cells in sections. * Criterion function Such function is determined as the minimum task execution cost in relation to the number of tested algorithms by the task: \[ \begin{array}{l}\text{F}(x,c)=\min\left\{C_{1}\big{(}x_{11}/na_{1}+x_{12}/ na_{1}+x_{13}/na_{1}+\ldots+x_{1j}/na_{1}+\right.\\ \left.C_{2}\big{(}x_{21}/na_{2}+x_{22}/na_{2}+x_{23}/na_{2}+\ldots+x_{2j}/na_{2 }+\right.\\ \left.C_{3}\big{(}x_{31}/na_{3}+x_{32}/na_{3}+x_{33}/na_{3}+\ldots+x_{3j}/na_{3 }+\right.\\ \left.\ldots+\right.\\ \left.C_{i}\big{(}x_{i1}/na_{i}+x_{i2}/na_{i}+x_{i3}/na_{i}+\ldots+x_{ij}/na_{i }\right\}\end{array} \right.\end{array}\] (5) where:
* \(C_{i}\)--implementation cost of the \(i\) task;
* \(na_{i}\)--number of algorithms tested in a row using a given check;
* \(x_{ij}\)--coordinates of individual algorithm cells in sections. **An embodiment of a test determination method*
* Let there be a determined task matrix with determined execution costs. The task is to conduct tests checking the correct implementation of points-switching functions for the station track system in question. With possible movements from under home signals A and B, it is possible to move to station tracks 1, 2, and 4. Only the fragment that contains points elements should be taken into account from the entire sheet. This is already the first minimization stage depending on the check objective. The task specifies points testing, and therefore, the task sheet is (Figure 5):  
The control and monitoring algorithm matrix is as follows:  
\[ \begin{array}{l}x_{13}x_{16}x_{18}x_{19}x_{23}x_{25}x_{211}x_{33}x_{35}x_{3 12}x_{41}x_{47}x_{49}x_{52}x_{54}x_{55}x_{511}x_{62}x_{64}x_{65}x_{612}\end{array}  \tag{6}\]  
Figure 5: Locking sheet in the notation of control and monitoring algorithms (a points section 1–6). Let us write the coordinates \(x_{ij}\) of all used algorithms (\"1\"):  
* \(x_{13}\) corresponds to the cell with algorithm a21 for points 2 in the A1 route to track 1;
* \(3_{1}\)--general costs of value 3 in the A1 task. By applying the conditions:
* Not every check must be used, therefore: \[ \begin{array}{c}x_{13}+x_{16}+x_{18}+x_{19}\geq 0\\ x_{23}+x_{25}+x_{211}\geq 0\\ x_{33}+x_{35}+x_{312}\geq 0\\ x_{41}+x_{47}+x_{49}\geq 0\\ x_{52}+x_{54}+x_{55}+x_{511}\geq 0\\ x_{62}+x_{64}+x_{65}+x_{612}\geq 0\end{array} \] (9)
- Criterion function: \[\begin{array}{c}\text{F}(x,c)=\text{min}\ \{ \begin{array}{c}3\ (x_{13}/4+x_{16}/4+x_{18}/4+x_{19}/4+\\ 3\ (x_{23}/3+x_{25}/3+x_{211}/3+\\ 3\ (x_{33}/3+x_{35}/3+x_{312}/3+\\ 3\ (x_{41}/3+x_{47}/3+x_{49}/3+\\ 3\ (x_{52}/4+x_{54}/4+x_{55}/4+x_{511}/4+\\ 10\ (x_{62}/4+x_{64}/4+x_{65}/4+x_{612}/4\}\end{array} \] (10)  
A proprietary notation of the program, variables, restrictions, criterion function and computation results can be found below. Mathematica v12.3 software was employed for this purpose. The \(x_{\bar{\eta}}\) variables are written as coordinates, e.g., \(x_{13}\) in the Mathematica environment as PA1 Za21 (Route A1 Points 1 algorithm 21).