In: Petri Net Technology for Communication-Based Systems, pages 321-351. Volume 2472 of Lecture Notes in Computer Science / Hartmut Ehrig, Wolfgang Reisig, Grzegorz Rozenberg and Herbert Weber (Eds.) --- Springer-Verlag, November 2003.
Abstract: Petri net variants are widely used as a workflow modelling technique. Recently, UML activity diagrams have been used for the same purpose, even though the syntax and semantics of activity diagrams has not been yet fully worked out. Nevertheless, activity diagrams seem very similar to Petri nets and on the surface, one may think that they are variants of each other. To substantiate or deny this claim, we need to formalise the intended semantics of activity diagrams and then compare this with various Petri net semantics. In previous papers we have defined two formal semantics for UML activity diagrams that are intended for workflow modelling. In this paper, we discuss the design choices that underlie these two semantics and investigate whether these design choices can be met in low-level and high-level Petri net semantics. We argue that the main difference between the Petri net semantics and our semantics of UML activity diagrams is that the Petri net semantics models resource usage of closed, active systems that are non-reactive, whereas our semantics of UML activity diagrams models open, reactive systems. Since workflow systems are open, reactive systems, we conclude that Petri nets cannot model workflows accurately, unless they are extended with a syntax and semantics for reactivity.