Improvement of Suboptimal Siphon- and FBM-Based Control Model of a Well-Known ${\rm S}^{3}{\rm PR}$

Siphon-based deadlock control of Flexible Manufacturing System (FMS) runs faster by avoiding reachability analysis, but reaches fewer states than an optimal. First-met bad marking (FBM) method requires more monitors, but reaches more states by refining some monitors with smaller (hence less disturbed) controller regions. However, the same refinement leads to more monitors for other siphons, which can be combined without losing states. This paper develops the formal theory to uncover the secret behind the above discrepancy. It improves the siphon-based approach to reach more states while using fewer monitors.