Semantics, Verification, and Implementation of Workflows ... - YAWL

Chapter 3. OR-join semantics
c1
B
c4
A
c2
C
c5
E
F
c3
D
c6
Figure 3.3: A YAWL net modified from Figure 3.2
therefore, E is enabled at M. So, even though two active paths are chosen after
OR-split task A, the OR-join evaluation should not wait for tokens from both
paths, as it is possible that not all the tokens are on the path to an OR-join task.
c1
C
c6
c4
A
c2
B
E
c5
c3
D
c7
Figure 3.4: A YAWL net with two OR-join tasks C and D
B_c5
i c1+c2+c3 c1+c3+c4+c5
B_c4,c5
B_c4
c1+c3+c5
c1+c3+c4
D
C
C
D
D
C
c1+c7
c3+c5+c6
c1+c4+c7
c3+c6
C
D
C
D
c6+c7
E
o
Figure 3.5: The reachability graph of the YAWL net in Figure 3.4
Next, the behaviour of OR-joins is described using an example with one ORsplit
and two OR-joins. The example in Figure 3.4 demonstrates a net with
AND-split task A, AND-join task E, OR-split task B and OR-join tasks C and
D. The graph of Figure 3.5 shows the reachable markings from the initial marking
i to the end marking o. A node in the reachability graph represents a reachable
marking and an edge represents a task that is executed to reach that particular
marking. First consider a marking M = c1 + c2 + c3 where there is a token in
input condition c1 of OR-join task C and in input condition c3 of OR-join task D
in addition to the token in input condition of task B. To determine whether tasks
C and D should be enabled at M, we need to find out whether either condition c4
or c5 is marked in the reachable markings from M. We can see that by executing
task B, it is possible to reach markings c1 + c3 + c5 or c1 + c3 + c4 + c5 that
mark c5, an input condition of task D not marked in M. Alternatively, markings
PhD Thesis – c○ 2006 M.T.K Wynn – Page 35