Process Instances
The discussion of state transition diagrams is extended from a localized view
of individual tasks to a process view. In order to do this, a number of definitions
are required. The first definition extends the compact representation
of extended workflow nets in a way that it syntactically complies with the
workflow net definition: wherever there is an arc connecting two tasks in an
extended workflow net, a new condition is added and the arcs are modified
accordingly.
Definition
Let N = (C, i, o, T, F, split, join, rem, nofi) be an extended
workflow net.
• Cext
N is an extended condition set, such that
Cext
= C [ {cij |(ti, tj) 2 F \ T × T}
The extended condition set and the extended flow relation are shown in
Figure 4.62. Observe that for each direct connection between tasks in the
original extended workflow net, one condition and the respective arcs are
added: Cext
1 = {i1, cAB, cBC, cCD, cCE, cCF , cDG, cEG, cFG, o1}.
The extended flow relation Fext
1 is given by the arrows in Figure 4.62. Analogously,
the extended condition set and the extended flow relation for W2 are
given by Cext
2 = {i2, cHI , o2} and Fext = {(i2,H), (H, cHI ), (cHI , I), (I, o2)}.
Since there are multiple process instances for which tasks are being executed,
the identity of these cases needs to be taken into account when describing
the state of tasks and their task instances. Therefore, the following
assumptions concerning process identifiers are made.
Each process instance has a unique case identifier.
Each task instance has a unique task instance identifier.
Identifiers are structured to allow for child/parent relationships. This
means that each task instance identifier can be associated with its process
instance or case.
I denotes the set of identifiers.
Based on case identifiers and the state transition system discussed above, a
workflow state can be characterized as a bag of tokens, where each token has
condition and a case identifier.
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