Petri Nets have been popular among the developers of workflow management systems for more than twenty years [5
]: even if we do not consider the early work of Petri himself and Anatol Holt on modelling procedures with Petri Nets, Paul Zisman and Clarence Ellis adopted Petri Nets for modelling workflows in the late seventies. From those early years, there has been a growing amount of proposals adopting different classes of Petri Nets as the modelling framework of a workflow management system. The main reasons of the popularity of Petri Nets are the following:
they allow to give to workflow models a univocal non ambiguous semantics;
they have an easy to read graphical representation;
they may support a hierarchy of abstraction levels;
they are executable models, well suited for both simulation and software specifcation.
Today workflow technology, even if it is still considered as a hot technology whose success is imminent, has not yet gained large shares of the computer-based applications’ market. Trying to explain this apparent paradox, all its components (the workflow engine, the workflow models and the workflow design environment) have been deeply discussed [1
] Workflow models (and within them, also Net models) have been criticized for the following reasons:
they are too rigid since, by imposing an explicit flow of actions, they hinder users in overcoming breakdowns;
they are too complicated, since their design requires a professional expert and cannot be performed by users themselves.
On the contrary, it has been claimed that, in order to become the kernel of really usable workflow management systems, workflow models should have the following features:
they should be easily modifiable, supporting both the automatic verification of change correctness and safe change enactment on the ongoing instances ;
they should support exception handling, allowing users to follow exceptional paths on the basis of the policy of their organization, without making models too complicated;
they should offer multiple diverse views of the workflow to their diverse users (perfomers, managers, customers, designers).
I claim that Net Theory offers a very powerful platform for satisfying the above requirements, going far beyond the modelling capabilities that have been exploited in the workflow models developed up to now. In particular, I think that process extensions, net morphisms and synthesis algorithms provide powerful mathematical tools for dealing with the above requirements. In the Milano workflow management system [3
] we have used a subclass of Elementary Net Systems [7
], that has efficient algorithms for all the above services, for creating simple workflow models, that are easily changeable, allow exceptional paths and support a variety of views on the workflow [2
]. Even if we claim that workflow management systems do not need more powerful models, since simplicity is a positive attribute for them (at least with respect to a large class of workflows), there are several other classes of processes (production and logistics processes, juridical processes, ...), which may need modelling capabilities that go beyond the subclass of Elementary Net Systems we have chosen for the Milano Workflow Management System. The search for classes of Net Systems well supported by efficient algorithms is therefore open [4