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

Chapter 2. Formal foundations
Definition 2.31 (Irreducible cancellation regions) Let N be an eYAWL-net.
N satisfies the irreducible cancellation regions property iff for all x ∈ ran (rem),
x is not a reducible cancellation element w.r.t some task t in dom (rem) 9 .
An OR-join task is said to be convertible, when it could be better represented
as either an XOR-join or an AND-join task. Such tasks arise in two circumstances:
(i) when it is never possible to reach a marking which marks more than one
input condition of the task and (ii) when all input conditions of the task are
marked in all markings that enables the OR-join task. The objective is to detect
unnecessary OR-join tasks at design time as the non-local semantics of OR-join
requires expensive runtime analysis. This can be detected by looking at markings
in the reachability set that enable an OR-join task. In Figure 2.12, OR-join task
D is only enabled when all input conditions are marked (due to an AND-split task
A) and therefore, D should be modelled as an AND-join instead of an OR-join.
Definition 2.32 (Convertible OR-join) Let N be an eYAWL-net and t be an
OR-join task in N. OR-join task t can be modelled as
• an XOR-join if only one condition in •t is ever marked in the enabling
markings of t, i.e., ∀ M∈N[Mi 〉(M[t〉 =⇒ ∃! p∈•t (M(p) > 0)),
• an AND-join if for all conditions in •t are always marked in the enabling
markings of t, i.e., ∀ M∈N[Mi 〉(M[t〉 =⇒ ∀ p∈•t (M(p) > 0)) 10 .
Figure 2.12: A YAWL net with a (convertible) OR-join task D
Definition 2.33 (Immutable OR-joins) Let N be an eYAWL-net. N satisfies
the immutable OR-joins property iff for all t ∈ T , join(t) = OR implies that t is
not a convertible OR-join.
In this section, formal definitions for a YAWL net and four structural properties
have been presented. In the next section, the mappings from YAWL to reset
nets are demonstrated.
9 dom means the domain of a function and ran means the range of a function
10 We are using here the reset net notation of reachable markings for YAWL. The formal
semantics of the OR-join is defined in Chapter 3.
PhD Thesis – c○ 2006 M.T.K Wynn – Page 27