## 5 Conclusions  
A novel decomposition method of Petri net-based CPS aimed at the integrated systems was proposed in the paper. The presented technique is based on linear algebra and involves place invariants computation in order to obtain sequential components (SMCs). Contrary to the existing decomposition methods, the proposed algorithm is strictly aimed at the designer's needs. Therefore, the selection of particular components is executed manually. The proposed idea was validated experimentally, with the use of integrated device. In particular, a beverage production and distribution cyber-physical system was modelled by a Petri net, decomposed with the presented concept, and finally implemented within an FPGA device.  
Besides the benefits mentioned above, there are also limitations to the proposed technique. First of all, obtaining the sequential components can be exponential in the worst case. This means, that in the case of extremely complex systems, decomposition may take a long time. On the other hand, introduced manual selection may essentially speed-up this process, since the designer is able to interrupt the process once the obtained components cover all places of the modelled CPS. Furthermore, the proposed method is strictly oriented on integrated systems. Nevertheless, since the decomposed components form sequential automata, they can be applied to distributed systems. However, in such a case, more  
Figure 5: Summary of synthesis and implementation of the CPS (**left**), and the utilised Nexys 4 DDR board (**right**).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Device Resources** & **Utilization** \\ \hline LUTs blocks & 25 of 63,400 (<1\%) \\ Flip-flops & 27 of 126,800 (<1\%) \\ IO blocks & 26 of 210 (12\%) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Utilization of FPGA device resources.  
advanced synchronisation mechanisms ought to be provided, since components may work in different time-domains. Therefore, this is an excellent starting point for future works.  
In particular, plans for the future include the development of the decomposition algorithm oriented on the distributed systems. This means that the CPS can be implemented within several devices, e.g., a set of connected microprocessors such as Arduinos, PLCs, etc. Besides splitting the system into sequential components, such a method ought to include proper synchronisation between devices in order to assure proper functionality of the whole CPS.  
Conceptualization, R.W. and A.C.; Methodology, R.W., A.C. and M.W.; Software, R.W.; Validation, R.W. and M.W.; Formal analysis, R.W. and A.C.; Investigation, R.W., A.C. and M.W.; Resources, R.W., A.C., M.W. and M.M.; Data curation, R.W.; Writing--original draft, R.W. and M.W.; Writing--review & editing, R.W., A.C. and M.W.; Visualization, R.W. and M.M.; Supervision, R.W. and A.C.; Project administration, R.W.; Funding acquisition, R.W. and A.C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by NATIONAL SCIENCE CENTRE, POLAND, grant number 2019/35/B/ST6/01683. This research was funded (in part) by the Portuguese FCT program, Center of Technology and Systems (CTS) UIDB/00066/2020/UIDP/00066/2020. The APC was funded by [PERSON] and [PERSON].  
Not applicable.  
The authors declare no conflict of interest.