Apart from these rules, there are also two YAWL reduction rules that do take the OR-join into account. As one of these rules is a specialization of the other, we start with the more general rule: the fusion of incoming edges to an OR-join (FOR1) rule. This rule is quite similar to the fusion of parallel conditions rule and the fusion of alternative conditions rule, but Requires only one split task and one join task, while the other two rules allow for multiple splits and joins, and
20 Verification 531 EST ... FST FSC FPT ... ... ... FAT ... ... ... FPC ... ... ... FAC ... ... ... FAAT ... FXXT ... Fig. 20.10 A visual representation of all reduction rules for YAWL without OR-joins Allows for the join construct to be an OR-join, while the parallel rule requires an AND-join and the alternative rule an XOR-join. Given a set of conditions, which contains at least two conditions, an OR-join task, and an arbitrary split task, this rule can remove all-but-one of the conditions. Provided that:
532 E. Verbeek and M. Wynn FOR1 ... FOR2 ... Fig. 20.11 A visual representation of both OR-join rules The conditions are being canceled by the same set of tasks The OR-join task is the output of every condition from the set The other task is the input of every condition from the set The OR-join task is not on some cycle with any other OR-join task, then we can remove all-but-one of these conditions. The OR-join task is allowed to have additional inputs, while the other task is allowed to have additional outputs. The OR-join is indifferent to the number of conditions in-between any preceding task and itself, as long as there is at least one. Therefore, we can simply remove all-but-one of them. The second rule is a specialization of this rule, as it: Forbids the OR-join task to have additional inputs, Forbids the other task to have additional outputs, Forbids both tasks to have a (nonempty) cancelation region, and Forbids the OR-join to be on some cycle with some other OR-join task. Using the fusion of incoming edges to an OR-join (FOR2) rule, we can now first remove all-but-one conditions in-between both tasks, which leaves only one input place for the OR-join. As a result, this OR-join decorator can be removed, and the fusion of series tasks rule can then be applied to reduce the condition and one of the tasks. However, because of the middle step (removing an OR-join decorator), this rule is not just a combination of both other rules. Figure 20.11 visualizes both rules. After having applied all these soundness-preserving reduction rules over and over again, the resulting state space could be considerably smaller than the original state space. This could have a positive effect on the verification of the soundness proper- ties, which all are based on this state space. Nevertheless, there is no guarantee that the resulting state-space is even finite in size, let alone be small enough to make the verification feasible. In such situations, we can use structural transition invariants that can be used to approximate the relaxed soundness property and diagnose the YAWL net based on this approximation.
20 Verification 533 20.5