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Workflow nets (WF-nets)
Workflow nets (WF-nets) are a subclass of Petri nets intending to model the workflow of process activities. The WF-net transitions are assigned to tasks or activities, and places are assigned to the pre/post conditions. The WF-nets have additional structural and operational requirements, mainly the addition of a single input (source) place with no previous transitions, and output place (sink) with no following transitions. Accordingly start and termination markings can be defined that represent the process status.

WF-nets have the soundness property, indicating that a process with a start marking of k tokens in its sink place, can reach the termination state marking with k tokens in its sink place (defined as K-sound WF-net). Additionally, all the transitions in the process could fire (i.e., for each transition there is a reachable state in which the transition is enabled). A general sound (G-sound) WF-net is defined as being K-sound for every k>0.

A directed path in the Petri net is defined as the sequence of nodes (places and transitions) linked by the directed arcs. An elementary path includes every node in the sequence only once.

A Well-handled Petri net is a net in which there are no fully distinct elementary paths between a place and a transition (or transition and a place), i.e., if there are two paths between the pair of node then these paths share a node. An acyclic well-handled WF-net is sound (G-sound).

Extended WF-net is a Petri net that is composed of a WF-net with additional transition t (feedback transition). The sink place is connected as the input place of transition t and the source place as its output place. Firing of the transition causes iteration of the process (Note: the extended WF-net is not a WF-net). WRI (Well-handled with Regular Iteration) WF-net, is an extended acyclic well-handled WF-net. WRI-WF-net can be built as composition of nets, i.e., replacing a transition within a WRI-WF-net with a subnet which is a WRI-WF-net. The result is also WRI-WF-net. WRI-WF-nets are G-sound, therefore by using only WRI-WF-net building blocks, one can get WF-nets that are G-sound by construction.

The Design structure matrix (DSM) can model process relations, and be utilized for process planning. The DSM-nets are realization of DSM-based plans into workflow processes by Petri nets, and are equivalent to WRI-WF-nets. The DSM-net construction process ensures the soundness property of the resulting net.

DSM Net
DSM nets are represented by a subclass of Petri nets, utilizing this mathematical process modeling technique for interpretation of the DSM-based process plans, into a consistent workflow process model.