Petri Nets as Zero-Degree Asynchronous Control Systems

In this note, we define asynchronous discrete control systems of degree zero, which, under certain additional conditions, can be considered as a generalization of Petri nets. In this interpretation, Petri nets are considered from the very beginning as discrete dynamic systems of a special type, described in the state space. In particular, the proposed representation of Petri nets completely excludes the use of graphs (with somewhat intimidating notions of places, transitions, tokens, markings and transition rules), which may appeal to a certain category of readers. This generalization, of course, does not pretend to be an effective replacement for the traditional “graphical” approach, but at the same time allows us to look at Petri nets from a more general point of view and, in addition, provides a useful geometric necessary condition for reachability problem.