BPMN and Beyond Business process modelling notation, workflow ...

that it does not depend only on the (static) diagram structure. In fact the following is required:
“Process flow SHALL continue when the signals (Tokens) arrive from all of the incoming Sequence
Flow that are expecting a signal based on the upstream structure of the Process . . . Some of the
incoming Sequence Flow will not have signals and the pattern of which Sequence Flow will have
signals may change for different instantiations of the Process.” [15, p.80] Generally it is claimed in
the literature that the “non-locality leads to serious problems when the formal semantics of the ORjoin
has to be defined” [24, p.3]. The discussion of and the importance attached to these “problems”
in the literature is partly influenced by a weakness of the underlying Petri-net computation model,
which has well-known problems when dealing with non-local (in particular if dynamic) properties. 16
In reality the issue is more a question of process design style, where modeling and verification of
desired process behavior go hand in hand via modular (componentwise) definitions and reasoning
schemes, which are not in need of imposing static structural conditions (see [5]). It is only to a
minor extent a question of defining the semantics of OR-joins. In fact, in the ASM framework one
can succinctly describe various ways to dynamically relate the tokens produced by an OR-Split
node to the ones consumed by an associated OR-Join node. See [14].
4.5 BPMN Instances of Gateway Rules
In BPMN gateways are classified into exclusive (XOR), inclusive (OR), parallel (AND) and complex.
The case of complex gateways is treated below.
An AND gateway of BPMN can be used in two ways. When it is used ‘to create parallel flow’,
it has the behavior of AndSplitGateTransition, where each outgoing arc represents a gate
(without loss of generality we assume the BPMN Best Practice Normal Form, i.e. a gateway with
one incoming arc). The so-called merge use of the AND gateway of BPMN ‘to synchronize parallel
flow’ has the behavior of AndJoinGateTransition.
The data-based XOR and the OR gateway of BPMN, when ‘acting only as a Merge’, both
have only one gate without an associated GateCond or GateEvent; the event-based XOR is forbidden
by the standard to act only as a Merge. Thus those two gateway uses are an instance of
OrJoinGateTransition where select Consume is restricted to yield either an empty set (in which
case the rule cannot fire) or
for XOR a singleton set,
for OR a subset of the incoming arcs with associated tokens ‘that have been produced upstream’
[15, p.80] 17 .
This satisfies the standard document requirement for XOR that in case of multiple incoming
flow, the incoming flow which in a step of the gateway has not be chosen ‘will be used to continue
the flow of the Process (as if there were no Gateway)’; similarly for OR [15, p.75].
When acting as a split into alternatives, the XOR (in its two versions data-based and eventbased)
and the OR gateway of BPMN are both an instance of OrSplitGateTransition where
select Produce is restricted to yield one of the following:
For the data-based XOR a singleton set consisting of the first out ∈ outArc(node), in the given
order of gates, satisfying GateCond(out). If our understanding of BPMN is correct then in this
case DataCond(node, O) = GateCond(out) and EventCond(node, O) = true.
For the event-based XOR a singleton set O consisting of the first out ∈ outArc(node), in the
given order of gates, satisfying GateEvent(out). If our understanding of BPMN is correct then
in this case EventCond(node, O) = GateEvent(out) and DataCond(node, O) = true.
For OR a non-empty subset of the outgoing arcs.
16 Similar problems have been identified in [36] for the mapping of UML 2.0 activity diagrams to Petri
nets.
17 The BPMN document provides no indications for determining this subset, which has a synchronization
role.
14