xoEPC - Jan Mendling

74 3. Event-driven Process Chains (EPC)
propagated, and this way the initial situation is reproduced. This can be repeated again
and again. Without a sequence of two phases, the transitions could continue infinitely
and the result would be undefined.
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i1 o1
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(a) initial wait context (b) input context changes to dead (c) the loop is dead
Figure 3.15: Propagating dead context in a loop
The precedence of the two phases can also be motivated using an example EPC con-
taining a loop. The propagation of dead context with only one dead input is needed to
accurately mark loops as dead. Figure 3.15 shows the picture of a simple loop with one
XOR-join as entrance and one XOR-split as exit. Initially, the loop might be in a wait
context (a). If the path to the loop becomes dead, this context is propagated into the loop
(b) and to its output (c). If not all join-connectors would propagate dead context with one
dead input, the loop could never become dead. But since this often results in too many
dead arcs, the wait context propagation must be performed afterwards. It guarantees that
arcs that can still be receive a positive token get a wait context.
Phase 3: Negative Token Propagation
Negative tokens can result from branches that are not executed after OR-joins or start
events. The transition relation for negative token propagation includes four firing rules
that consume and produce negative tokens. Furthermore, the output arcs are set to a dead
context. Figure 3.16 gives an illustration of the transition relation. All transitions can
only be applied if all input arcs hold negative tokens and if there is no positive token on
the output arc. In the following section, we will show that this phase terminates.
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