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Modelling interfaces with oWFN : Open workflow nets represent asynchro-
nous communication, along message ports, with the order of sent messages not
necessarily preserved upon their arrival: A message port contains an unordered
set of messages (just as your home letter box). Even more, two different messages
may have identical content, i.e., cannot be distinguished in any respect. The
messages in a port thus constitute a bag (i.e. a finite multiset). This is the most
liberal and general form of asynchronous communication, and the most common
form in the world of business processes.
Modeling internal control with oWFN : An open workflow net is not confined
to sequential control, but may very well exhibit concurrent control flow. This is
most useful: Firstly, composition of two oWFNs results in an oWFN again, with
the previous components' two flows of control merged into internal concurrent
control of flow of the composed system.
Secondly, languages such as WS-BPEL anyway exhibit concurrent control
flow. This can adequately be modeled in the framework of oWFN.
4.2
The Formal Framework of Open Workflow Nets
Technically, an open workflow net N is a conventional Petri net with distin-
guished input and output places to store input and output messages during
computation. Consequently, an input place has no ingoing arcs in N ,andan
output place no outgoing arcs. Furthermore, an oWFN has an initial marking
m 0 and a set Ω of final markings. Summing up, an oWFN can be written as
N =( P,T,F,in,out,m 0 ) ,
,amarking m 0 and a set Ω of markings. 1
Graphically we extend the classical Petri net representation by an encompass-
ing dotted line. The input and output places are located on the line's surface.
The initial marking is explicitly represented. The final markings have to be de-
scribed elsewhere. Figure 2 shows an example.
P , in = out =
with in, out
According to the usual notions of Petri nets, a step
t
m
m
of an oWFN N transforms a marking m into a marking m , following the well-
known occurrence rule for transitions t .A run of N is a sequence
t 1
−→
t 2
−→
... t k
m 0
m 1
−→
m k
t i
−→
with m 0 the initial marking, m k a final marking, and m i− 1
m i astepof N
( i =1 ,...,k ).
1 We assume the reader's familiarity with elementary notions of Petri nets. The ap-
pendix provides formal details.
 
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