In the literature, elementary system nets are often extended by additional notations, especially
(“no transition can add an (
+ 1)th token to a place
”) and arc weights (“
tokens simultaneously flow through an arc”). We will discuss both of these extensions and show that they do not increase the expressiveness of elementary system nets: they can be simulated and are thus merely syntactic sugar. Occasionally, it is possible to use capacities and arc weights to construct very intuitive and clear models. In such cases, they should definitely be used.
However, a transition that is supposed to “test” the number of tokens in a place, or that should be given priority in case of a conflict, is a different matter: such things cannot be simulated within the bounds of elementary system nets.