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

Chapter 2. Formal foundations
c C,D
Figure 2.8: An example E2WF-net for the net in Figure 2.7
explicit EWF-net (E2WF-net) for the net in Figure 2.7. Note that a new condition
c C,D has been introduced. We denote the set of conditions extended to include
implicit conditions as C ext , and denote the extended flow relation as F ext . We
now define an explicit extended workflow net (E2WF-net) using C ext and F ext as
follows:
Definition 2.27 (E2WF-net) Let N = (C, i, o, T, F, split, join, rem, nofi) be
an EWF-net, the corresponding explicit EWF-net (E2WF-net) is defined as
(C ext , i, o, T, F ext , split, join, rem, nofi) where
C ext = C ∪ {c (t1 ,t 2 ) | (t 1 , t 2 ) ∈ F ∩ (T × T )} and
F ext =(F \ (T × T ))
∪{(t 1 , c (t1 ,t 2 )) | (t 1 , t 2 ) ∈ F ∩ (T × T )}
∪{(c (t1 ,t 2 ), t 2 ) | (t 1 , t 2 ) ∈ F ∩ (T × T )}.
We assume that all EWF-nets considered are first transformed into E2WFnets.
The notion of preset, postset, markings, and others defined for a reset net
is also used for an E2WF-net. Similarly, the notion of initial and end markings
defined for an RWF-net is also used for an E2WF-net where i, o are input and
output conditions. Since, an EWF-net is just a formal terminology for a YAWL
net, we propose to use the synonym “YAWL net” for an EWF-net. Similarly, we
propose to use the term “eYAWL-net” (explicit YAWL net) for an E2WF-net.
2.3.2 Structural properties
Four structural properties of an eYAWL-net: soundness, weak soundness, irreducible
cancellation regions, and immutable OR-joins are presented next.
An eYAWL-net is sound if and only if it satisfies the following three criteria:
option to complete, proper completion and no dead tasks. The soundness
property of an eYAWL-net (Definition 2.28) is closely related to the soundness
property of an RWF-net (Definition 2.22). The only difference is the type of
model being considered (RWF-net vs eYAWL-net).
Definition 2.28 (Soundness) Let N be an eYAWL-net and M i , M o be the initial
and end markings. N is sound iff:
1. option to complete: for every marking M reachable from M i , there exists
an occurrence sequence leading from M to M o , and
PhD Thesis – c○ 2006 M.T.K Wynn – Page 23