Marking homothetic monotonicity and fluidization of untimed Petri nets

On the Petri Nets with a Single Shared Place and Beyond

“…However, generally, numerous fundamental properties, including liveness, reversibility, boundedness and deadlockfreeness, are not preserved upon any increase of the initial marking, see e.g. [3,35,36,6]. In Figure 4, we show that live, unit-weighted H1S systems are not always m-live nor m-reversible, taking inspiration from Figure 1 On the left, a live and reversible H1S-WMG ≤ system.…”

“…We also plan to implement our techniques in a model-checker and complete this work with a series of benchmarks on much more complex use-cases. A complementary objective is to investigate the combination of our methods with the reduction techniques developed in [45], as well as separability [39,40] and marking homothety [36], always with the aim of improving their efficiency and of widening their applicative area.…”

“…For any system (N, M 0 ), in case M 0 can be divided by some positive integer k, the behavior of (N, M 0 ) can sometimes be deduced from the behavior of (N, M 0 /k), while checking the latter is generally much less costly. This idea is related to separability [39,40] and to the homothetic markings studied in [36], a relationship with the fluidized version of the net being also investigated in the latter.…”