Contents
From the Editors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Imprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Cover Picture Story
Jetty Kleijn and Maciej Koutny:Report on PETRI NETS 2009 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Work in Progress
Ana Juhásová and Gabriel Juhás:Soundness of resource constrained workflow nets is decidable . . . . . . . . . . . . . . . . 5
L.M. Hillah, E. Kindler, F. Kordon, L. Petrucci, and N. Trèves:A primer on the Petri Net Markup Language and ISO/IEC 15909-2* . . . . . . . . . . . . 9
Recent Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Order Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Gesellschaftfür Informatik e.V.
Deadline for next volume: March 30, 2010
Petri Net Newsletter
G
Newsletter of the Volume 76Special Interest Groups on ISSN 03911804
Petri Nets andRelated System Models October 2009
Contents
From the Editors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Imprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Cover Picture Story
Jetty Kleijn and Maciej Koutny:Report on PETRI NETS 2009 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Work in Progress
Ana Juhásová and Gabriel Juhás:Soundness of resource constrained workflow nets is decidable . . . . . . . . . . . . . . . . 5
L.M. Hillah, E. Kindler, F. Kordon, L. Petrucci, and N. Trèves:A primer on the Petri Net Markup Language and ISO/IEC 15909-2* . . . . . . . . . . . . 9
Recent Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Order Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Gesellschaftfür Informatik e.V.
Deadline for next volume: March 30, 2010
Petri Net Newsletter
G
Newsletter of the Volume 76Special Interest Groups on ISSN 03911804
Petri Nets andRelated System Models October 2009
From the editors
We regret that the april 2008 issue did not appear due to financial problems.For the next years, the issues are secured now.
In this issue of the Petri Net Newsletter we present two publications,both in the “work in progress”-section. The first publication, “Soundness ofRessource Constrained Workflow Nets is Decidable” by Gabriel Juhás andAna Juhásová, presents an algorithm to decide soundness in a more generalsetting as considered so far in literature. The second publication is a reporton the Petri Net Markup Language (PNML) as it is defined in ISO/IEC15909-2, written by L.M. Hillah, E. Kindler, F. Kordon, L. Petrucci and N.Trèves. It aims for unifying the different lines of PNML. This report was al-ready presented at the CPN workshop, Aarhus, Denmark, in October 2009,and is reproduced in this issue of the Petri Net Newsletter as an invitationfrom the editors to bring the results to a broader audience.
Moreover, the issue contains a short report on the Petri Nets Conference2009 in Paris written by Jetty Kleijn and Maciej Koutny. The cover pictureshows a nice photo of Gregorz Rozenberg (shooted by Andrey Mokhov), af-ter his invited lecture in Paris.
As in the last issue from october 2008, the bibliography with the latestpublished papers on Petri nets turned out to be too long to include it in thisissue in the usual way including abstracts. Therefore, we decided to omitthe abstracts. Still, the bibliography including abstracts is availabe online.
Please note, that beginning with this issue, Ekkart Kindler at his wish isnot longer co-executive-editor. We would like to thank him heartly for thelong years of essential support.
On behalf of all editors,
Augsburg, October 2009Robert Lorenz
1
Imprint: “Petri Net Newsletter” · c© October 2009 · ISSN 0931-1084 · 300 copies printedThe Petri Net Newsletter is an information service of the Special Interest Group FG 0.0.1“Petri Nets and Related System Models” of the Gesellschaft für Informatik (GI), Bonn,Germany. Two issues are being published per year. The editorial board of the Petri NetNewsletter is formed by:
Jörg Desel Daniel MoldtEkkart Kindler Rüdiger ValkKurt Lautenbach Karsten WolfRobert Lorenz
Scope: The Petri Net Newsletter serves as a medium for the rapid distribution of anyinformation about Petri Nets and related system models all over the world. Topicsinclude:
• reviewed technical contributions including surveys and state-of-the-art-reports• work in progress including problems and puzzles• reports on departments, institutes, companies, projects, local activities• information about new books and PhD thesis• abstracts of recent publications
Subscription: Members of FG 0.0.1 of the GI receive one copy of the Newsletter free ofcharge. On the last page of this issue, you will find an application form containing theaddress of the GI. Additional and former issues can also be obtained from the GI.
Contributions: Any contributions to the field are welcome. It should be clearly statedwhether a contribution is submitted as a technical contribution or as work in progress.Papers submitted as technical contributions will be reviewed. They should be 6 to15 pages long and in A4 format. Articles submitted as work in progress will not bereviewed. As contributions will be printed as submitted, make sure that no space iswasted. Contributions should be sent to:
Robert LorenzLehrprofessur für Informatik, Universität AugsburgUniversitätsstrasse 2, 86159 Augsburg, [email protected]
Conference Announcements and Conference Reports: Conference announce-ments such as Calls for Papers and Calls for Registration are no longer in the focusof the Petri Net Newsletter. On special request, they will still be published. They shouldbe formatted according to the layout of the Newsletter and take at most 2 pages.
Recent Publications: In the newsletter, the new entries of the online Petri Net Bib-liography (see http://www.informatik.uni-hamburg.de/TGI/pnbib/) are printed. Thebibliography is maintained by Frank Heitmann. To keep the bibliography as complete aspossible, please send new bibliography entries by e-mail to: [email protected] containing name of author(s), title, book, ... , and abstract.
Deadlines: There are two issues per year. Deadlines are the end of March and the endof September.
2
Report onPETRI NETS 2009
22-26 June, 2009, Paris, France
Jetty Kleijn Maciej KoutnyLeiden University Newcastle University
The 30th International Conference on Application and Theory of Petri Netsand Other Models of Concurrency was organized by Fabrice Kordon andhis team from the MeFoSyLoMa group at the campus de Jussieu of theUniversite Pierre et Marie Curie. MeFoSyLoMa stands for Formal Methodsfor Software and Hardware Systems and involves laboratories from differentParisian institutions. The Petri net conference was co-located with RSP 2009,the 20th IEEE/IFIP International Symposium on Rapid System Prototyping.There were eleven satellite events. The collaborative effort of MeFoSyLoMatook care of a smoothly run operation and provided friendly support forparticipants and lecturers.
The two conferences shared five keynotes: Joseph Sifakis (Turing Award2007) who lectured on component-based construction of heterogeneous real-time systems; Grzegorz Rozenberg who presented reaction systems as a for-mal framework for processes based on biochemical reactions; Bernard Cour-tois considered past and future of prototyping of custom circuits and systems;Bill Tonti discussed rapid system deployment using the IEEE technology nav-igator. Unfortunately, the fifth speaker, Gabriel Juhas, fell ill just a few daysbefore the conference and was unable to attend.
The program committee of Petri Nets, chaired by Giuliana Franceschinisand Karsten Wolf, accepted 19 papers (including 5 tool papers) out of 46submissions from 20 different countries. The proceedings have appeared asvolume 5606 in the LNCS series and some authors were invited to publish anextended, full version of their paper in a special issue of the journal Funda-menta Informaticae. The best paper award (presented at the closing session)went to Fernando Rosa-Velardo and David de Frutos-Escrig for their paperon decidability results for Petri nets with name creation and replication.
Both Petri Nets and RSP were officially opened on Wednesday. All satel-lite events took place on Monday and Tuesday June 22 and 23. There wasan introductory tutorial on Petri Nets (Jorg Desel, Susanna Donatelli, KurtJensen and Jetty Kleijn) as a precursor to the modular Petri Net Courseenvisaged for 2010. In addition, the Workshops and Tutorials committee
3
chaired by Susanna Donatelli and Maciej Koutny, selected four more ad-vanced tutorials: Continuous Petri Nets, a special tutorial in honour of LauraRecalde, who passed away in December 2008, organized by Manuel Silva,Alessandro Giua, and Serge Haddad; BioModel Engineering - from Struc-ture to Behaviour, organized by Monika Heiner, David Gilbert, and RainerBreitling; Evaluating Concurrent Software Architectures Using Petri Nets,organized by Rob Pettit; PNML, the Petri net Markup Language, Theoryand Practice, organized by Ekkart Kindler and Lom Hillah.RSP had two tutorials: Computer Aided Formal Verification and Validation(by Bret Michael) and System-Level Modeling and Validation of Continuous/Discrete Systems (by Gabriela Nicolescu).
Four workshops were organized in association with the Petri net con-ference: PNSE’09, International Workshop on Petri Nets and Software En-gineering (chair Daniel Moldt); ORGMOD’09, International Workshop onOrganizational Modeling (chairs Daniel Moldt, Olivier Boissier and MichaelKohler-Bußmeier); TiSto’09, International Workshop on Timing and Stochas-ticity in Petri Nets and Other Models of Concurrency (chairs Andras Horvathand Olivier Roux); APNOC’09 International Workshop on Abstractions forPetri Nets and Other Models of Concurrency (chairs Natalia Sidorova andAlexander Serebrenik).Authors of some of the best workshop papers will be invited to submit arevised version to be considered for inclusion in a volume of ToPNoC, Trans-actions on Petri Nets and other models of Concurrency, an LNCS subseries.
Petri Nets, RSP and the associated events had a total of 222 attendees,including 75 students. Almost half of the participants came from France. Weall enjoyed very much the reception offered by the city of Paris in the mag-nificent Hotel de Ville. On Thursday, the visit of the Architecture Museumin the Palais de Caillot, close to the Tour Eiffel, had excellent timing as ittook place during heavy showers. Afterwards, the sky was clear again whenwe had a lovely dinner cruising the Seine.To get a further impression of Petri Nets 2009, have a look athttp://petrinets2009.lip6.fr/medias/closing-pn2008.movhttp://petrinets2009.lip6.fr/index.php?page=photos
Petri Nets 2010, organized by Joao Fernandes, will take place in Braga,Portugal. It will be co-located with ACSD, the International Conference onApplication of Concurrency to System Design.See http://acsd-petrinets2010.di.uminho.pt/?page=PetriNets2010
4
Soundess of resource constrained workflow nets is decidable
Ana Juhasova
Faculty of Electrical Engineering
and Information Technology
Slovak University of Technology Bratislava
Gabriel Juhas
Faculty of Electrical Engineering
and Information Technology
Slovak University of Technology Bratislava
Abstract
In the paper we show how to transform the problem of
dynamic soundness of resource constrained workflow nets
(rcwf-nets) to reachability and home state property of p/t
nets. As these properties are decidable, the same holds for
dynamic soundness of rcwf-nets.
1. Introduction
Workflow nets (wf-nets) are a prominent formalism to
model and analyze workflow processes [1]. Their main
power in comparison with other modelling techniques is the
possibility to find errors in processes in a formal way [4].
Classical wf-nets do not consider soundess analysis w.r.t.
several cases and constrained number of resources. In prac-
tice, the question of soundness with considering constrained
number of resources remains crucial. To formalize the prob-
lem we follow the conncept of static and non-static places
introduced in [3] resulting in resource constrained workflow
nets. For better illustration, one can choose a similarity with
the instances in the object-oriented programming: A rcwf-
net can be understood as a class definition, with static places
corresponding to the static variables shared by all instances
(i.e. shared resources holders) and non-static places as well
as transitions corresponding to the non-static variables and
methods of instances, which are no more shared by single
cases. Thus, each case creates its own copy of non-static
places, transitions and respective arcs. We consider a sit-
uation, where marking of the static places before and after
case handling remains unchanged. We provide definition
which is fully builded on low-level Petri nets [5], with a
comparison to [3], where coloured nets [6] with token id-s
are used.
2. Place/transition nets and workflow nets
In this section we introduce basic notions for
place/transition nets and workflow net following [5] and [1].
Definition 1 (Place/transition net). A place/transition net
(shortly a p/t net) is a quadruple (P, T, F,W ), where P is
a finite set of places, T is a finite set of transitions such that
P ∩ T = ∅, F ⊆ (P × T ) ∪ (T × P ) is a flow relation and
W : F → N is a weigth function1. As usual, we extend the
weight function W to pairs of net elements (x, y) satisfying
(x, y) 6∈ F by W (x, y) = 0. Let (P, T, F,W ) be a p/t net
and let x ∈ P ∪ T . Then •x = {y ∈ P ∪ T | (y, x) ∈ F}is called preset of x and similarly x• = {y ∈ P ∪ T |(x, y) ∈ F} is called postset of x. Marking of a p/t net
(P, T, F,W ) is a function m : P → N. A pair (PN,m0),where PN = (P, T, F,W ) is a p/t net and m0 : P → N is
its marking, is called a marked p/t net and m0 is reffered as
the initial marking of the marked p/t net.
Places are graphically depicted by circles, transitions by
boxes, elements of the flow relation by arcs, values of the
weigth function by labels of arcs and values of a marking
of a place by the appropriate number of black tokens in the
place. As usual, labels of the arcs corresponding to the val-
ues of the weigth function equal to 1 are ommited.
Definition 2 (Occurrence rule). Let N = (P, T, F,W ) be a
p/t-net. A transition t ∈ T is enabled to occur in a marking
m of N iff m(p) ≥ W (p, t) for every place p ∈ •t. If
a transition t is enabled to occur in a marking m, then its
occurrence leads to the new marking m′ defined by m′(p) =
m(p)−W (p, t)+W (t, p) for every p ∈ P . We write mt−→
m′ to denote that t is enabled to occur in m and that its
occurrence leads to m′.
Definition 3 (Occurrence sequence, Reachability). Let
N = (P, T, F,W ) be a p/t-net and m be a marking of N . A
finite sequence of transitions σ = t1 . . . tn, n ∈ N is called
1where N denotes nonnegative integers
5
an occurrence sequence enabled in m and leading to mn if
there exists a sequence of markings m1, . . . ,mn such that
mt1−→ m1
t2−→ . . .tn−→ mn.
The marking mn is said to be reachable from the marking
m.
In a marked p/t-net, markings reachable from the initial
marking m0 are shortly called reachable markings and de-
noted my [m0〉.
Definition 4 (Workflow net). A p/t net PN = (P, T, F.W )is called a workflow net (shortly a wf-net) iff: There exist a
place in ∈ P with •in = ∅ ∧ i• 6= ∅ called an input place
and a place out ∈ P with out• = ∅ ∧ •out 6= ∅ called
an output place. Moreover, ∀p ∈ P \ {in, out} : •p 6=∅∧p• 6= ∅. Let min denote a marking of the wf-net such that
min(in) = 1 and m(p) = 0 for each p ∈ P \{in} and mout
denote a marking of the wf-net such that mout(out) = 1 and
m(p) = 0 for each p ∈ P \ {out}.
In the following definition of soundness we relax the re-
quirement that each transition has to be used at least in one
branch of the process, as this requirement is not important
for our further discussion.
Definition 5 (Soundness of a wf-net). A wf-net PN =(P, T, F,W ) is sound iff
• for each m reachable from mi there holds: mout is
reachable from m
• for each m reachable from mi there holds: if
m(out) = 1 then m = mout, i.e. mout is the
only marking reachable from min with marked output
place.
A well known fact is that soundness of wf-nets is de-
cidable and a sound wf-net has finite number of reachable
markings, see e.g. [1].
Lemma 6. Let PN be a wf-net. Then the soundness of
PN is decidable and if PN is sound then the number of
markings reachable from min in PN is finite.
3. Resource constrained workflow nets
In this section we introduce resource constrained work-
flow nets motivated by [3]. In comparison to [3] we al-
low more types of resources and do require the number of
resources not changed before and after a case is handled,
whereas in [3] the number of resources is bounded by the
initial value.
Definition 7. Let PN = (P, T, F,W ) be a wf-net. Let
P = S∪D with S∩D = ∅ and in, out ∈ D. Set S denotes
2 2
2
d1
s1
d3
d2 d4
inout
t2
t1 t3 t5
t4 t6
Figure 1. A rcwf-net
non-static places and set S denotes the static places (shared
resource holders). Let m0 be a marking of PN such that
m0(d) = 0 for each d ∈ D \ {in} and m0(in) = 1. Then
marked p/t net (PN,m0) is called resource-constrained wf-
net (shortly rcwf-net). By mf we denote a marking of rcwf-
net called final marking given by: mf (d) = 0 for each
d ∈ D \{out}, mf (out) = 1 and mf (s) = m0(s) for each
s ∈ S.
Static places (also called resource places in [3]) are de-
picted in figures by circles with shadow.
An example of a rcwf-net is given in Figure 1. It models
a simple process of treating patient in an emergency depart-
ment. Marking of the static place s1 stands for the number
of available doctors. Transition t1 stands for a decision that
a case is complicated and two doctors are necessary to treat
the patient, therefore it produces 2 tokens to place d1. Tran-
sition t3 means that a doctor goes to treat a patient who
needs two doctors. Number of tokens in place d3 stands
for the number of doctors treating the patient. Transition
t5 means that two doctors finished to treat the patient and
are available again. The branch with places and transitions
indexed by even numbers model the treating of a patient
where only one doctor is needed.
Obviously, at a given moment of time several cases (in-
stances) of a process described by a rcwf-net can be han-
dled. This is expressed by so called run-time nets of rcwf-
nets.
Definition 8 (Run-time nets of an rcwf-net). Let (PN =(P = (S∪D), T, F,W ),m0) be a rcwf-net and n ∈ N. Let
P ′ = S ∪ (D × {1, . . . , n}), T ′ = T × {1, . . . , n},
F1 = {((x, i), (y, i)) ∈ ((D1, . . . , n) × T ′) ∪ (T ′ × (D ×1, . . . , n)) | (x, y) ∈ F},
F2 = {(x), (y, i)) ∈ (S×T ′) | (x, y) ∈ F ∧ i ∈ 1, . . . , n},
F3 = {(x, i), (y)) ∈ (T ′×S) | (x, y) ∈ F ∧ i ∈ 1, . . . , n},
F ′ = F1 ∪ F2 ∪ F3
and let W ′ : F → N be given by:
∀((x, i), (y, i)) ∈ F1 : W ((x, i), (y, i)) = W (x, y)∀((x), (y, i)) ∈ F2 : W ((x), (y, i)) = W (x, y)∀((x, i), (y)) ∈ F3 : W ((x, i), (y)) = W (x, y).Let m′
0 : P ′ → N denote a marking satisfying:
6
m′0(s) = m0(s) for each s ∈ S and m′
0(d, i) = m0(d) for
each (d, i) ∈ D × {1, .., n}).Then the marked p/t net (PN ′ = (P ′, T ′, F ′,W ′),m′
0) is
called the run-time net of rcwf-net (PN,m0) for n cases.
By m′f we denote a marking of run-time net (PN ′,m′
0) of
rcwf-net (PN,m0) called final marking given by: mf (d) =0 for each d ∈ P ′\(S∪({out}×{1, . . . , n}), mf (out, i) =1 for each i ∈ {1, . . . , n} and mf (s) = m0(s) for each
s ∈ S.
Dynamic soundness expresses the property saying that
for any number of cases the process modelled by respective
run-time net will terminate properly.
Definition 9 (Dynamic soundness of rcwf-nets). Let n ∈ Nand (PN,m0) be a rcwf-net and (PN ′,m′
0) be the run-
time net of rcwf-net (PN,m0) for n cases. Then rcwf-net
(PN,m0) is sound for n cases iff:
• For each m′ : P ′ → N reachable from m′0 in
(PN ′,m′0) there holds: m′
f is reachable from m′;
• For each m′ reachable from m′0 in (PN ′,m′
0) and
each i ∈ {1, . . . , n} there hods: m′(out, i) = 1 ⇒(∀d ∈ D : m′(d, i) = 0).
An rcwf-net (PN,m0) is dynamically sound if for each n ∈N there holds: (PN,m0) is sound for n cases.
Using lemma 6 we get that a necessary condition for
rcwf-net to be dynamically sound is that it has finite number
of reachable markings.
Corollary 10. Let (PN,m0) be a rcwf-net. It si decid-
able whether (PN,m0) is sound for 1 case. If (PN,m0)is sound for 1 case then the number of markings reachable
from m0 in (PN,m0) is finite.
As it is illustrated in Figure 3, the rcwf-net from Figure
1, which is sound for 1 case is not dynamically sound as
it is not sound for 3 cases. The question is, whether the
dynamic soundess is decidable in general. The paper [3]
gives an algorithm for a restricted class of rcfw-nets with
just one static place. In [3] it is mentioned that a rcwf-net
with one static place can be transformed to a state machine
via its reachability graph. It is claimed that the original net
is sound iff the transformed is. Unfortunately, [3] does not
formalize the transormation and the mentionned result and
the algorithm for checking soundess is provided for state
machines with one static place only. Here we formalize
the transformation mentined in [3] and show that dynamic
soundness is decidable in general. Namelly, problem re-
duces to reachability problem and the home state problem
of the transformed net. Remember that a necessary condi-
tion for dynamic soundness of a rcwf-net given by Corollary
10 is that it is sound for 1 case and in particular the num-
ber of reachable states in the rcwf-net is finite (rcwf-net is
bounded).
2 2
2
22
22
2
2
s1
(d4,1)(d2,1)
(d1,1)
(in,1)(out,1)
(d3,1)
(out,2)
(d3,2)
(d2,2)
(d1,2)
(d4,2)
(in,2)
(out,3)
(d3,3)
(d4,3)
(in,3)
(d1,3)
(d2,3)
(t1,1)
(t6,1)(t2,1)
(t5,1)
(t4,1)
(t3,1)
(t4,2) (t6,2)
(t5,2)(t3,2)
(t2,2)
(t1,2)
(t4,3)(t2,3)
(t1,3)
(t6,3)
(t3,3) (t5,3)
Figure 2. Run-time net for 3 cases
2 2
2
22
22
2
2
s1
(d4,1)(d2,1)
(d1,1)
(in,1)(out,1)
(d3,1)
(out,2)
(d3,2)
(d2,2)
(d1,2)
(d4,2)
(in,2)
(out,3)
(d3,3)
(d4,3)
(in,3)
(d1,3)
(d2,3)
(t1,1)
(t6,1)(t2,1)
(t5,1)
(t4,1)
(t3,1)
(t4,2) (t6,2)
(t5,2)(t3,2)
(t2,2)
(t1,2)
(t4,3)(t2,3)
(t1,3)
(t6,3)
(t3,3) (t5,3)
Figure 3. Deadlock of the run-time net for
3 cases after firing (t1, 1), (t1, 2), (t1, 3) and
(t3, 1), (t3, 2), (t3, 3).
7
2
2d1+3s1
s1
2d3+s1
d2+3s1 d4+2s1
in+3s1 out+3s1
(in+3s1,t2,d2+3s1)
(in+3s1,t1,2d1+3s1) (d1+d3+2s1,t3,2d3+s1) (2d3+s1,t5,out+3s1
(d2+3s1,t4,d4+2s1) (d4+2s1,t6,out+3s1)
d1+d3+2s1
(2d1+3s1,t3,d1+d3+2s1)
source
put
stop
empty
Figure 4. The transformed rcwf-net
Definition 11. (Transformed rcwf-net) Let (PN =(P = S ∪ D,T, F,W ),m0) be a rcwf-net with a
finite number of markings reachable from m0. Let
source, put, stop, empty /∈ S∪ [m0〉∪ ([m0〉×T × [m0〉).P tr = S ∪ [m0〉 ∪ {source},
T tr = {(m1, t,m2) ∈ [m0〉 × T × [m0〉 | m1t−→
m2} ∪ {put, stop, empty},
F tr = {(m, (m1, t,m2)) ∈ ([m0〉 × T tr) | m = m1}∪{((m1, t,m2),m) ∈ (T tr × [m0〉) | m = m2}∪{(s, (m1, t,m2)) ∈ (S × T tr) | (s, t) ∈ F}∪{((m1, t,m2)s) ∈ (T tr × S) | (t, s) ∈ F}∪{(source, stop), (source, put), (put, source), (put,m0),(mf , empty)}.
Let W tr : F tr → N be given as fol-
lows: W tr(x, (m1, t,m2)) = W (x, t) and
W tr((m1, t,m2), x) = W (t, x) whenever x ∈ S,
otherwise W tr(f) = 1. Let mtr0 : P tr → N be defined
by: mtr0 (s) = m0(s) for each s ∈ S, mtr
0 (source) = 1and mtr
0 (m) = 0 for each m ∈ [m0〉 . Then marked p/t net
(PN tr = (P tr,T tr, F tr,W tr),mtr0 ) is called transformed
net of rcwf-net (PN,m0). By mtrf we denote a marking
mtrf : P tr → N satisfying mtr
0 (s) = m0(s) for each s ∈ S
and mtr0 (x) = 0 for each x ∈ P tr \ S.
The example of the transformed net of the rcwf-net from
Figure 1 is in Figure 4.
We get the following main result.
Theorem 12. Let (PN,m0) be a rcfn-net. (PN,m0) is dy-
namically sound if and only if (PN,m0) is sound for 1 case
and in transformed net (PN tr,mtr0 ) of rcwf-net (PN,m0)
the marking mtrf is reachable from any marking mtr reach-
able from mtr0 (i.e. mtr
f is home state of (PN tr,mtr0 )).
Because reachability and home-state are decidable in p/t
nets [2], we get the following corollary.
Corollary 13. Let (PN,m0) be a rcfn-net. Testing dy-
namic soundness of (PN,m0) is decidable.
4. Further research
One line of further research is oriented to find an effec-
tive algorithm to check dynamic soundness based on the
2
22
d1
s1
d3
d2 d4
inout
t2
t1 t3 t5
t4 t6
s2
Figure 5. A corrected minimally restrictive dy-
namically sound rcwf-net
special structure of the transformed net. Another line of
research is to find an algorithm constructing a minimally
restrictive dynamically sound rcwf-net for an original rcwf-
net, which is not dynamically sound. An example of such a
net for the net from Figure 1 is given in Figure 5.
Acknowledgement
Supported by the project APVV-0618-07 of the Slovak
Research and Development Agency.
References
[1] W.M.P. van der Aalst and K. van Hee. Workflow Man-
agement, Models Methods and Systems. The MIT
Press, Cambridge, Massachusetts, 2002.
[2] J. Esparza and M. Nielsen. Decidability issues for
Petri nets–a survey. J. Inform. Process. Cybernet. 30
(3), pp. 143-160, 1994.
[3] K. M. van Hee, A. Serebrenik, N. Sidorova and
M. Voorhoeve. Soundness of Resource-Constrained
Workflow Nets. ICATPN 2005, LNCS 3536, Springer,
pp. 250-267, 2005.
[4] J. Medling and W.M.P. van der Aalst. Errors in the
SAP Reference Models. BPTrends. June 2006.
[5] J. Desel and G. Juhas. What is a Petri Net? In
H. Ehrig, G. Juhas, J. Padberg, G. Rozenberg (Eds.):
Unifying Petri Nets, LNCS 2128, Springer, pp. 1–25,
2001.
[6] K. Jensen. Coloured Petri Nets. Basic Concepts, Anal-
ysis Methods and Practical Use I II III. Springer,
1997.
8
A primer on the Petri Net Markup Language andISO/IEC 15909-2∗
L.M. Hillah, UPMC & CNRS UMR 7606, ParisE. Kindler, Technical University of Denmark (DTU), Lyngby
F. Kordon, UPMC & CNRS UMR 7606, ParisL. Petrucci, University Paris 13 & CNRS UMR 7030, Villetaneuse
N. Trèves, CNAM & Cedric, Paris
1 IntroductionIn 2000, there was a workshop [1] that should foster the definition of a standard transfer format for Petrinets as a satellite event of the annual ‘Petri Net Conference’ in Aarhus. As a result of this first workshop,after many other discussions and meetings, the Petri Net Markup Language (PNML) is about to be finallyadopted as ISO/IEC 15909-2. Over the years, PNML has evolved and, unfortunately, there are manydifferent intermediate versions and variants, that are still in use. With this paper, we would like to reporton the final result and on PNML as it is defined in ISO/IEC 15909-2. This way, we hope to unify thedifferent lines of PNML and advertise the use of ISO/IEC 15909-2.
Note that this paper is not a copy or exact reproduction of ISO/IEC 15909-2 (which, including allAnnexes, has more than 100 pages). Rather it is a restructured excerpt that focuses on the most importantissues and abstracts from some technical details, which can be found in ISO/IEC 15909-2. Most of thetechnical details can be derived from the RELAX NG grammars provided at the PNML web pages [17].Together, this should provide a fair account of the standard, its ideas and concepts, and its practical use.For a in-depth discussion of the rationales and design decisions behind PNML, we refer to the bunch ofearlier publications [2, 15, 4, 18, 19]
Though not an exact copy of ISO/IEC 15909-2, this paper reuses material of ISO/IEC 15909-2 withsome modifications and simplifications with the kind permission of ISO/IEC, Geneva.
Originally, PNML was introduced as an interchange format for all kinds of Petri nets [2, 3, 4]. Somemajor concepts of PNML were driven by this objective. Technically, ISO/IEC 15909-2 defines a transfersyntax for High-level Petri Net Graphs and those subclasses of Petri nets only that have been conceptuallyand mathematically defined in the International Standard ISO/IEC 15909-1 [5], for capturing the essenceof all kinds of coloured and high-level Petri nets [6, 7, 8, 9, 10, 11, 12, 13]. In this paper, the focus ison PNML for high-level nets in order not to mix up concepts that are part of ISO/IEC 15909-2 and someextensions, which are currently under consideration for ISO/IEC 15909-3. In the conclusion (Sect. 5), wewill briefly discuss some of these perspectives, which make PNML applicable for all kinds of Petri nets.
2 ConceptsIn this section, we discuss the main concepts of PNML, were the main idea is that any kind of Petri netcan be considered to be a labelled graph. In particular, all information that is specific to a particular kindof Petri net can be captured in labels.
This will be discussed in more detail in Sect. 2.1. The concepts of PNML will be defined by a meta-model for PNML in terms of UML class diagrams. These meta-models, however, do not define the XMLsyntax for the transfer format. Therefore, there is a mapping from the concepts of the PNML meta-model
∗This paper was presented at the CPN workshop, Aarhus, Denmark, in October 2009, and is reproduced in the Petri NetNewsletter as a kind invitation from the editors.
9
PNML Core Model
SymmetricNetPT−Net HLPNG
<<merge>>
<<merge>>
<<merge>>
Figure 1: Overview of the UML packages of PNML
to XML, which will be discussed in Sect. 4. Curious readers, who are interested in looking at the actualXML right away, might have a look at this and, in particular, at the example in Listing 1.
As mentioned above, ISO/IEC 15909-2 defines transfer formats for different versions of Petri nets:Place/Transition Nets, High-level Petri Net Graphs (HLPNG), and Symmetric Nets as defined in ISO/IEC15909-1, where Symmetric Nets are a subclass of high-level nets, which originally were introduced underthe name well-formed nets [14]. The main differences between them are the available data types, whichwill be discussed in Sect. 3.
2.1 General PrinciplesIn order to deal with different kinds of Petri nets, the transfer format needs to be flexible and extensible.In order to obtain this flexibility, a Petri net is considered to be a labelled directed graph, where all typespecific information of the net is represented in labels. A label may be associated with a node, an arc, orthe net itself. This basic structure of a PNML Document is defined in the PNML Core Model using a UMLclass diagram. This will be discussed in Sect. 2.2.
The PNML Core Model imposes no restrictions on labels. Therefore, the PNML Core Model can representany kind of Petri net. Due to this generality of the PNML Core Model, there can be even PNML Documentsthat do not correspond to a Petri net at all. For example, there could be labels from two different andeven incompatible versions of Petri nets within the same PNML Document. For a concrete version of Petrinets, the legal labels will be defined by extending the PNML Core Model with another meta-model thatexactly defines the legal labels of this particular type.
Technically, the PNML Core Model is a UML package, and there are additional UML packages for thedifferent Petri net types that extend the PNML Core Model package. ISO/IEC 15909-2 defines a packagefor Place/Transition Nets, a package for Symmetric Nets, and a package for High-level Petri Net Graphs,where the package for High-level Petri Net Graphs extends the package for Symmetric Nets. Therefore,every Symmetric Net is also a High-level Petri Net Graph.
Figure 1 gives an overview of the different packages defined and on their dependencies. The packagePNML Core Model defines the basic structure of Petri nets; this structure is extended by the packagefor each type. The PNML Core Model is discussed in Sect. 2.2 and the package PT-Net is discussed inSect. 2.3.1. The general concepts of High-level Petri Net Graphs will be discussed in Sect. 2.3.2. Thedifferent data types used in the different versions of high-level Petri nets are discussed in Sect. 3.1. Basedon these data types, the package SymmetricNet is discussed in Sect. 3.3.2 and the package HLPNG forgeneral High-level Petri Net Graph is defined in Sect. 3.3.3.
2.2 The PNML Core ModelFigures 2 and 3 show the meta-model of the PNML Core Model as a UML class diagram. The diagram ofFig. 2 focusses on the conceptual parts, whereas the diagram of Fig. 3 focusses on the parts concerningthe graphical representation (i. e. graphics). Note that the data type String is imported from a separatepackage XMLSchemaDataTypes, which is discussed in Sect. 2.2.6; since this is a technicality only, thereferences to this package are shown in tiny fonts in the diagram. The concepts of the PNML Core Modelare discussed below.
10
self.target.page self.source.page =
context Arc inv:
PNMLCoreModel
XMLSchemaDataTypes::
String
ToolInfo
toolversion
Object
id* label *
label *
*
net
object
{redefines label}name
0..1
name
0..1
{redefines label}
Graphics
Node
RefPlace RefTrans
1
1
Page
TransitionNode1
ref
1
ref
source
target
page
Transition
Arc
* *
*
*
page1..*
1..*
toolspecific
PetriNetDoc
Label
PetriNet
typeid
AttributeAnnotationName
PlaceNode
Place
−− source and target must−− be on the same page
*
1textgraphics
0..1
0..1graphics
toolspecific
toolspecific *
<<import>>
XMLSchemaDataTypes
Figure 2: The PNML Core Model package: concepts
2.2.1 Petri Net Documents, Petri Nets, and Objects
A document that meets the requirements of the PNML Core Model is called a Petri Net Document(PetriNetDoc) or a PNML Document. It contains one or more Petri Nets (PetriNet). Each Petri Nethas a unique identifier and a type. The type is a name uniquely identifying a Petri net type definition;an example for such a name is http://www.pnml.org/version-2009/grammar/ptnet for the definitionof Place/Transition Nets.
A Petri net consists of one or more pages that in turn consist of several objects. These objects,basically, represent the graph structure of the Petri net. Each object within a Petri net document has aunique identifier, which can be used for referring to this object. Moreover, each object may be equippedwith graphical information defining its position, size, colour, shape and other attributes on its graphicalappearance (graphics). The precise graphical information that can be provided for an object depends onthe particular type of the object (see Sect. 2.2.4 for more details).
The most important objects of a Petri net are places, transitions, and arcs. For extensibility reasonsand principles of good design, places and transitions are generalised to nodes. For reasons explained inSect. 2.2.2, this generalisation is via place nodes and via transition nodes. Nodes of a Petri net can beconnected by arcs.
Note that it is legal to have an arc from a place to a place or from a transition to a transition accordingto the PNML Core Model. The reason is that there are versions of Petri nets that support such arcs. If aPetri net type does not support such arcs, this restriction will be defined in the particular package defining
11
this type.
2.2.2 Pages and Reference Nodes
Three other kinds of objects are used for structuring a Petri net : pages, reference places, and referencetransitions. As mentioned above, a page may contain other objects; since a page is an object itself, a pagemay even contain other pages, thus defining a hierarchy of subpages.
Note that PNML requires that an arc must connect nodes on the same page only. The reason for thisrequirement is that arcs connecting nodes on different pages cannot be drawn graphically. In the PNMLCore Model of Fig. 2, this requirement is captured by the OCL expression next to the class for arcs.
In order to connect nodes on different pages by an arc, a representative of one of the two nodes mustbe drawn on the same page as the other node. Then, this representative may be connected with the othernode by an arc. This representative is called a reference node, because it has a reference to the node itrepresents. Note that a reference place must refer to a place or a reference place, and a reference transitionmust refer to a transition or a reference transition. Moreover, cyclic references among reference nodes arenot allowed.
2.2.3 Labels
In order to assign further meaning to an object, each object may have labels. Typically, there are labelsrepresenting the name of a node, the initial marking of a place, the transition condition, or some arcannotation. In addition, the Petri net itself or its pages may have some labels, which are called globallabels. For example, the package HLPNG defines declarations as global labels of a High-level Petri Net,which are used for defining variables, and user-defined sorts and operators.
In the PNML Core Model, we distinguish two kinds of labels: annotations and attributes. An annotationcomprises information that is typically displayed as text next to the corresponding object. Examples ofannotations are names, initial markings, arc annotations, transition conditions, and timing or stochasticinformation. In contrast, an attribute is, typically, not displayed as text next to the corresponding object.Rather, an attribute has an effect on the shape or colour of the corresponding object. For example, anattribute such as arc type could have domain {normal, read, inhibitor, reset}. ISO/IEC 15909-2,however, does not mandate the effect on the graphical appearance of an attribute.
Note that the classes for label, annotation and attribute are abstract in the PNML Core Model, whichmeans that the PNML Core Model does not define concrete labels, annotations, and attributes. The onlyconcrete label defined in the PNML Core Model is the name, which is a label that can be used for anyobject within any Petri net type. This way, any object such as nodes, pages, the net itself, and evenarcs can have a name. The value of a name is a String, which is imported from the separate packageXMLSchemaDataTypes (see Sect. 2.2.6 for more information). All other concrete labels are defined in thepackages for the concrete Petri net types (see Sect. 2.3).
In order to support the exchange of information among tools that have different textual representationfor the same concepts (i. e. when they have different concrete syntax), there are two ways for representingthe information within an annotation: textually in some concrete syntax and structurally as an abstractsyntax tree (see Sect. 2.3.2 and 4.1.2 for details).
Note that reference nodes may have labels, but these labels do not have any meaning. This choice wasmade in order to obtain a semantically equivalent Petri net without pages by merging every referencenode to the node it directly or indirectly refers to. This is called flattening of the Petri net (see [15] fordetails). Still, the labels of a reference node can have an effect on the graphical appearance or can givesome additional information to the user.
2.2.4 Graphical Information
In addition to the Petri net concepts, information concerning the graphical appearance can be associatedwith each object and each annotation. For a node, this information includes its position; for an arc, itincludes a list of positions that define intermediate points of the arc; for an object’s annotation, it includesits relative position with respect to the corresponding object ; for an annotation of a page, the positionis absolute. There can be further information concerning the size, colour and shape of nodes or arcs, orconcerning the colour, font and font size of labels. Note that this information can be used for automaticallytransforming a Petri Net into Scalable Vector Graphics (SVG) by XSLT transformations (see [16] for moredetails). This transformation, however, is not part of ISO/IEC 15909-2.
12
Figure 3 shows the different graphical information that can be attached to the different types of objectsand the different attributes. Note that these concepts still belong to the PNML Core Model ; it is shown ina different figure only in order to avoid clutter. Table 1 gives an overview of the meaning and the domainof the attributes of the different graphical features.
Line
shapecolorwidthstyle
Font
familystyleweightsizedecorationalignrotation
context ArcGraphics inv: self.object.oclIsKindOf(Arc)
self.object.oclIsKindOf(Page) self.object.oclIsKindOf(Node) orcontext NodeGraphics inv:
context AnnotationGraphics inv: self.object.oclIsKindOf(Annotation)
NodeGraphics AnnotationGraphics
0..1 font
line0..1
fill0..1 0..1
fill
colorimage
gradient−rotation
line0..1
line
0..1
0..10..1dimension
*position
position
offset
0..1xy
Coordinate
PNMLCoreModel
{ordered}
gradient−color
Graphics
Fill
ArcGraphics
Figure 3: The PNML Core Model : graphical information
Table 1: PNML attributes of graphical informationClass Attribute Domain
Coordinate x decimaly decimal
Fill color CSS2-colorimage anyURIgradient-color CSS2-colorgradient-rotation {vertical, horizontal, diagonal}
Line shape {line, curve}color CSS2-colorwidth nonNegativeDecimalstyle {solid, dash, dot}
Font family CSS2-font-familystyle CSS2-font-styleweight CSS2-font-weightsize CSS2-font-sizedecoration {underline, overline, line-through}align {left, center, right}rotation decimal
The position defines the absolute position for nodes and pages. For an annotation the offset definesits relative position to the object it is attached to; for a global annotation, the offset defines the absoluteposition on that page. Each absolute or relative position consists of a pair of Cartesian coordinates (x, y),where the units are points (pt). As for many graphical tools, the x-axis runs from left to right and they-axis from top to bottom. And the reference point for the position of an object is its centre.
For an arc, the (possibly empty) sequence of positions defines its intermediate points (bend points).Note that the positions of the start point and the end point of an arc are not given explicitly for thearc. These positions are determined from the position of the source and the target nodes of the arc andthe direction of the first resp. last segment of the arc, by the intersection of this segment with the nodes
13
border. Altogether, the arc is displayed as a path from the start point on the border of the source node tothe end point on the border of the target node via the intermediate points. Note that, even though thereis no way to define the start point and the end point of an arc explicitly, the above concepts allow a usermaking sure that an arc starts and ends exactly at the point, where he wants it to start and end: If thefirst, (or last) intermediate point of an arc lies exactly on the border of the respective node, this will bethe start point (or the end point resp.) of that arc.
For arcs, there are also some line attributes, which define the style, the colour, and the width in whichthey are displayed.
Depending on the value of the attribute shape of element line, the path is displayed as a brokenline (polyline) or as a quadratic Bezier curve. In the case of a Bezier curve the intermediate positionsalternately are the line connectors or Bezier control points. The reference point of an arc is the middle ofthe arc, which is the middle of the middle segment of the arc, if there are an odd number of segments; itis the middle point, if there are an even number of segments.
The dimension of a node or page gives its size, again as a pair referring to its width (x) and height(y). Depending on the ratio of height and width, a place is displayed as an ellipse rather than a circle. Atransition is displayed as a rectangle of the corresponding size. If the dimension of an element is missing,each tool is free to use its own default value for the dimensions.
The two elements fill and line define the interior and outline colours of the corresponding element.The value assigned to a color attribute must be a RGB value or a predefined colour as defined by CSS2(Cascading Style Sheets 2). When the attribute gradient-color is defined, the fill colour continuouslyvaries from color to gradient-color. The additional attribute gradient-rotation defines the orientation ofthe gradient. When the attribute image is defined, the node is displayed as the image which is provided atthe specified URI, which must be a graphics file in JPEG or PNG format. In this case, all other attributesof fill and line are ignored.
For an annotation, the font element defines the font used to display the text of the label. The attributesfamily, style, weight, and size are CSS2 attributes for defining the appearance of the text. The detaileddescription of the possible values of these attributes and their effect can be found in the CSS2 specification.The decoration attribute defines additional properties of the appearance of the text such as underlining,overlining, or striking-through the text. Additionally, the align attribute defines the alignment of the textto the left, right or center. The rotation attribute defines a clockwise rotation of the text.
The reference point of an annotation is always its centre.
2.2.5 Tool Specific Information
For some tools, it might be necessary to store tool specific information (ToolInfo), which is not meant tobe used by other tools. In order to store this information, tool specific information may be associatedwith each object and each label. The internal structure of the tool specific information depends on the tooland is not specified by PNML. PNML provides a mechanism for clearly marking tool specific informationalong with the name and the version of the tool adding this information. Therefore, other tools can easilyignore it, and adding tool specific information will never compromise a Petri Net Document.
The same object may be tagged with tool specific information from different tools. This way, the samedocument can be used and changed by different tools at the same time. The intention is that a tool shouldnever change or delete the information added by another tool as long as the corresponding object is notdeleted. Moreover, tool specific information should be self-contained and not refer to other objects of thenet because the deletion of other objects by a different tool might make this reference invalid and leave thetool specific information inconsistent. This use of the tool specific information is strongly recommended;however, it is not normative.
2.2.6 Data Types
In this section, we discuss six XML data types, which are taken from XMLSchema. These can be used fordefining labels for some Petri net type with numerical and textual information. Note that these data typesare not related to the data types that may be used within high-level nets! Rather, they define the typesof the attributes and their XML syntax that may be used in the meta-models of the PNML Core Modeland of the Petri net types.
Figure 4 gives an overview of these XML data types and their relation.
14
NonNegativeDecimal
PositiveInteger
String
XMLSchemaDataTypes
NonNegativeInteger
Integer
Decimal
Figure 4: Standard data types
String refers to any printable sequence of characters, which is mapped to XML PCDATA. Decimals,NonNegativeDecimals, Integer, NonNegativeInteger, and PositiveInteger refer to any character sequencewhich denotes a number of the corresponding kind.
2.3 Petri Net Type Meta ModelsNext, we discuss three versions of Petri nets: Place/Transition Nets, Symmetric Nets, and High-LevelPetri Net Graphs (HLPNGs) as defined in ISO/IEC 15909-1, where Symmetric Nets1 are a restrictedversion of High-Level Petri Net Graphs currently defined as an Amendment to ISO/IEC 15909-1. Thegeneral relation between the different types has already been shown in Fig. 1. Again, the concepts ofthese different versions are defined in terms of meta-models. These meta-models define the labels of therespective Petri net type.
ISO/IEC 15909-1 defines a mapping from the concepts of Place/Transition Nets to the concepts ofHigh-Level Petri Net Graphs and shows how the usual mathematical representation of Place/TransitionNets can be represented as a restricted version of High-level Petri Nets. Though conceptually the samemodel, the syntax is different. Therefore, ISO/IEC 15909-2 introduces yet another Petri net version:Place/Transiton Nets in High-level Notation, which will be discussed in Sect. 3.3.1.
ISO/IEC 15909-2, however, introduces an explicit transfer format for Place/Transition Nets in ordernot to force tools for Place/Transition Nets to use the syntax of High-Level Petri Net Graphs. This formatreflects the usual mathematical definition of Place/Transition Nets.
2.3.1 Place/Transition Nets
Since Place/Transition Nets are the simplest version, we start with this version: the concepts are definedin terms of a meta-model in UML notation: the package PT-Net.
A Place/Transition Net is a net graph, where each place can be labelled with a natural numberrepresenting the initial marking and each arc can be labelled with a non-zero natural number representingthe arc annotation, with the usual meaning: the label of a place p denotes the initial marking M(p), thelabel of an arc f denotes the arc weight W (f).
Figure 5 shows the package PT-Net. Note that the only classes defined here are PTMarking andPTArcAnnotation. The classes Place, Arc, and Annotation come from the package PNML Core Model.They are imported (actually, they are merged) here in order to define the possible labels for the particularnodes of Place/Transition Nets. Likewise, the classes prefixed with XMLSchemaDataTypes are importedfrom the standard data type package (see Sect. 2.2.6).
The initial marking of a place is represented by the annotation PTMarking, the contents of whichmust be a non-negative integer. Technically, the representation of the contents of this label is defined byreferring to the data type NonNegativeInteger.
1Remember that Symmetric Nets were originally introduced under the name well-formed nets [14].
15
Place{redefines label}
initialMarking
PTMarking0..1
1text
Arc
XMLSchemaDataTypes::
NonNegativeInteger
PTArcAnnotation
PT−Net
text
Annotation
self.target.oclIsKindOf(PlaceNode) )
context Arc inv:
−− no arcs between nodes of the same kind
(self.source.oclIsKindOf(PlaceNode) and 1
PositiveInteger
XMLSchemaDataTypes::
{redefines label}
0..1
inscription
self.target.oclIsKindOf(TransitionNode) )
or
(self.source.oclIsKindOf(TransitionNode) and
XMLSchemaDataTypes
<<merge>> <<import>>
PNML Core Model
Figure 5: The package PT-Net
The arc annotation is represented by the annotation PTArcAnnotation, the contents of which mustbe a non-zero natural number, which is defined by referring to the data type PositiveInteger.
Note that, according to this definition, it is legal that a place does not have an annotation for theinitial marking. In that case, the initial marking is assumed to be empty, i. e. 0. Likewise, there may beno annotation for an arc. In that case, the arc annotation is assumed to be 1.
In addition to the definition of the new labels, this package also defines the structural restriction that,in a Place/Transition Net, an arc must not connect a place to a place or a transition to a transition. Thisis captured by the OCL expression below class arc.
Sometimes, one wants to store the position of the individual tokens within a place. In order not tomandate all tools to support this feature, ISO/IEC 15909-2 suggests a tool specific information for thispurpose, which would refer to the tool org.pnml.tool. Since no tool is required to support tool specificfeatures, every tool is free to use and support this feature or not.
PT−Net::
Coordinate
context TokenGraphics inv:
−− TokenGraphics only for PTMarkings
self.object.oclIsKindOf(PTMarking)
self.tool = ’org.pnml.tool’
PNML Extensions
* tokenposition
TokenGraphics
PT−Net::
ToolInfo
<<import>>PT−Net
Figure 6: Tool specific extension for token positions
This extension is shown in Fig. 6. For a PTMarking, this label can be equipped with the tool specificinformation attached to AnnotationGraphics. This consists of information on a list of tokenpositions.Each of these elements represents the position of a token relative to the centre of the place; represented as
16
a Coordinate, which is imported from package PT-Net, where it was obtained by a merge with the PNMLCore Model. If this graphical information is present at all, the number of tokenpositions should be thesame as indicated by the PTMarking (see example in Sect. 4.1.5).
2.3.2 High-Level Core Structure
ISO/IEC 15909-1 defines High-level Petri Net Graphs. Symmetric Nets and Place/Transition Nets areintroduced as restricted versions of High-level Petri Net Graphs. The difference is in the types and functionsthat may be used in the different versions. To cater for this structure, we distill the common structureof all High-level Petri Net Graphs first: This is called the High-Level Core Structure. The built-in datatypes of the specific Petri net types are discussed in Sect. 3.1.
Syntactically, the basic features of a High-Level Petri Net are the annotations of places, transitions,and arcs. For each place, a sort defines the type of the tokens on this place. A term associated with aplace denotes the initial marking and must have the respective sort. The term associated with an arcto or from a place, defines which tokens are added or removed, when the corresponding transition fires.These terms must also be of the respective sort.
For constructing such terms, one can use built-in operators and sorts, and user-defined variables,which are defined in a variable declaration. The variable declarations are annotations of the net or apage. Moreover, a transition can have a condition which is a term of sort boolean and imposes additionalconditions on the situations in which a transition can fire.
The meta-model for terms, which defines all these concepts, is shown in Fig. 7: It defines the conceptsof sorts, operators, declarations, and terms, and how terms are constructed from variables and operators.
UserSort
ProductSort
VariableDecl
name
Terms
SortDecl
name
MultisetSort
NamedSort
context NamedSort inv:
IsTypeOf(MultiSetSort)
!self.def.ocl.
context Operator inv:
−− sort of Term is output sort of Operator
self.sort = self.output
context Variable inv:
−− sort of Variable is sort of Term
self.sort = self.variableDecl.sort
1 /output
* /input
{ordered}equals(Sort):bool
1 variableDecl
1sort
1
Term
Sort Operator
*
BuiltInConst
BuiltInOperator
MultiSetOperator
BuiltInSort
UserOperator
OperatorDecl
name1declaration
*
1basis
elementSort
{ordered}
1def
1
declaration
{ordered}* subterm
1 def
*{ordered}
parameter
NamedOperator
multi
/sort
Variable
Declarations
Declaration
Tuple
Figure 7: The meta-model for Terms
For each variable declaration, there is a corresponding sort. A sort can be a built-in sort, a multiset sortover some basis sort, a product sort over some sorts, or a sort which is given in a user declaration. In thecore structure, the only possible sort declaration of a user is by constructing a new sort from existing ones
17
and by giving them a new name. From these, the user can define new ones. Note that cyclic references inuser-defined sorts are not allowed. In addition to these user-defined sorts, called named sorts, there willbe arbitrary sorts. Since these are not allowed in Symmetric Nets, these are not defined in the core. Theyare discussed in Sect. 3.3.3 where the concepts of general high-level nets are explained.
An operator can be a built-in constant or a built-in operator, a multiset operator which among otherscan construct a multiset from an enumeration of its elements, or a tuple operator. Each operator has asequence of sorts as its input sorts, and exactly one output sort, which defines its signature. As for sorts,the user can define his own operators. Here, it is only possible to define an abbreviation, which is calleda named operator : It can use a term, which is built from existing operators and parameter variables, fordefining a new operator. As for sorts, cycles (recursion) in these definitions are not allowed. As for sorts,there will be arbitrary operator declarations for High-level Petri Net Graphs, but not for Symmetric Nets.Therefore, these concepts will be discussed in Sect. 3.3.3.
From the built-in operators and the user-defined operators and variables, terms can be constructed inthe usual way. The sort of a term is the sort of the variable or the output sort of the operator. Therefore,sort is indicated as a derived association; its definition is expressed by an OCL expression in the UML meta-model. Note that the input and output sorts of the operator are also represented as derived associationsbecause, in some situations, they need not be given explicitly since they can be derived from the type ofthe operator.
Figure 8 shows the package High-Level Core Structure, which defines all the annotations for bothSymmetric Nets and High-Level Petri Net Graphs. Note that, since the classes for built-in sorts andoperators are abstract, we do not have any built-in sorts and operators yet. These are discussed inSect. 3.1.
In addition to the annotations defined above, the package High-Level Core Structure requires that arcsmust not connect two places and must not connect two transitions.
Note that this model defines an abstract syntax (composition structure) for all these concepts only. Inorder to allow tools to store the concrete text, all annotations of High-level Nets may also consist of text,which should be the same expression in the concrete syntax of some tool. This concrete syntax, however,is not mandated by ISO/IEC 15909-2; therefore, all the meaning is in the structure of the labels!
3 Details of High-level nets and their data typesAs mentioned earlier, Sect. 2.3.2 discussed the core structure of High-level Petri Net Graphs only. In thissection, we briefly discuss the details of the built-in sorts and operators. For each built-in sort, there is aUML package. Sections 3.1 gives an overview of these packages. Section 3.2 briefly discusses the packagefor user-defined declarations. Based on that, Sect. 3.3 defines the different types of high-level nets.
3.1 Data typesISO/IEC 15909-2 defines the following data types for being used in the different versions of high-levelPetri nets:
• Dots defines the sort which represents a type with exactly one element (token): {•}. This is usedto represent Place/Transition Nets as High-level Net Graphs.
• Multiset defines the multiset over any other sort, which are needed for defining the terms labellingarcs and for initial markings.
• Booleans defines the boolean type and associated operations.
• Finite Enumerations, Cyclic Enumerations, and Finite Integer Ranges allow the definition of finiteranges by explicitly enumerating them or by giving an integer range. Depending on the type, differentstructures are imposed on them [14], such as an order relation, or a successor and predecessoroperation.
• Partitions allow the definition of finite enumerations that are partitioned into sub-ranges, where apartition function defines for each element to which partition it belongs. These partitions define aseparate sort, where each partition is an element of the respective type.
18
−− the term for the condition must be of sort boolean
(self.structure.sort.oclIsKindOf(Booleans:Bool)
Place
Transition
PetriNet
Arc
Declaration
HLAnnotation
{redefines label}
declaration
*
HLCoreAnnotation
Annotation
Condition
self.target.oclIsKindOf(TransitionNode) )
or
(self.source.oclIsKindOf(TransitionNode) and
self.target.oclIsKindOf(PlaceNode) )
context Arc inv:
−− no arcs between nodes of the same kindcontext Condition inv:
Terms::Sort
Terms::Term
Page
Terms::Declarations
Terms::Term
XMLSchemaDataTypes::
String
(self.source.oclIsKindOf(PlaceNode) and
HLCoreStructure
*
Type structure
0..1
structure
structure
structure
0..1
0..1declaration
0..1
{redefines label}
type
{redefines label}
HLMarking0..1
structure{redefines label}
0..10..1
{redefines label}
condition
hlinitialMarking
0..1
0..1
{redefines label}
hlinscription
0..1
text
Terms::Term
<<import>>Booleans
<<import>>Terms
XMLSchemaDataTypes
<<merge>>
PNMLCoreModel
<<import>>
Figure 8: The package High-Level Core Structure
• Integer defines the integers and the usual operations on them; it also defines the subtypes positivenumbers and the natural numbers.
• Strings defines the strings and the usual operations on them.
• Lists defines the Lists over the other data types and the usual operations on them.
For details, we refer to ISO/IEC 15909-2 or to the RELAX NG grammars which can be found at [17].
3.2 User declarationsIn general High-Level Petri Net Graphs (HLPNGs), the user is allowed to define arbitrary sorts and op-erators. This package ArbitraryDeclarations is shown in Fig. 9. In contrast to named sorts and namedoperators, arbitrary sorts and operators do not come with a definition of the sort or operation; they justintroduce a new symbol without giving a definition for it. So, these symbols do not have a meaning, butcan be used for constructing terms.
19
The additional concept Unparsed in terms provides a means to include any text, which will not beparsed and interpreted by the tools. This is helpful for exchanging the general structure of a term, butnot all its details.
UnparsedTerms::Sort
Terms::DeclarationTerms::OperatorDecl
ArbitraryDeclarations
Terms::SortDecl
output
ArbitrarySort ArbitraryOperator
* input {ordered}
1
Terms
<<extends>>
Figure 9: The package ArbitraryDeclarations
3.3 Net typesBased on the data types introduced in the previous section, we can now discuss the different versions ofhigh-level nets. Note that, conceptually, high-level nets extend Place/Transition-Systems. But, syntacti-cally they do not. That is why all these types are not extending the package PT-Net, which is discussedin Sect. 2.3.1.
Instead, the different versions of high-level nets form a separate hierarchy (see also Fig. 1). The lowestlevel in this hierarchy are Place/Transition Nets in High-level Notation.
3.3.1 Place/Transition Nets as High-level Net Graphs
Booleans
<<import>>
<<merge>>
Multisets
Dots
HLCoreStructure
PT-HLPNGs<<import>>
<<import>>
Terms
<<import>>
<<import>>
<<import>>
context Type inv:
-- the type of all places must be Dot
self.structure.oclIsTypeOf(Dots::Dot)
context Condition inv:
-- the condition of all transitions must be true
let cond: Terms::Term = self.structure in
cond.oclIsTypeOf(Booleans::BooleanConstant) and
cond.value = ‘true’
Figure 10: The package of P/T Nets defined as restricted HLPNGs
Annex B of ISO/IEC 15909-1 defines Place/Transition Nets as a restricted form of High-level NetGraphs. Fig. 10 shows the corresponding UML definition. This class allows for the use of the built-in sortsBool and Dot only. It does neither allow any user declarations, nor variables, nor sorts, nor operators.
20
The type of each place must refer to sort Dot. All transition conditions need to be the constant true,if this label is present. And the arc annotations and the initial markings are ground terms of the mulitsetsort over Dot.
3.3.2 Symmetric Nets
Symmetric Nets as currently defined in an Amendment (Annex B.2) of Part 1 of ISO/IEC 15909, areHigh-Level Petri Net Graphs with some restrictions. Basically, the carrier sets of all basic sorts are finite,and only a fixed set of operations, as defined below, are allowed. Therefore, the sort of a place must notbe a multiset sort. The available built-in sorts are defined below.
Moreover, for Symmetric Nets, it is required that every HLPNG annotation has the structural informa-tion.
The built-in sorts of Symmetric Nets are the following: Booleans, range of integers, finite enumerations,cyclic enumerations and dots. Moreover, for every sort, there is the operator all, which is a multiset thatcontains exactly one element of its basis sort. This is often called the broadcast function.
Altogether, the Symmetric Nets can be defined by importing the packages as shown in Fig. 11.
!self.structure.oclIsKindOf(MultisetSort)
context Type inv:
−− no multiset sorts as types
<<import>>
<<import>>
<<import>>
<<import>>
<<import>>
<<import>>
<<import>>
<<merge>>
<<import>>
<<import>>
<<import>>
Booleans
Partitions
SymmetricNets
CyclicEnumerations
<<import>><<import>>
<<import>>
Multisets
FiniteEnumerations
<<import>>
FiniteIntRanges
Dots HLCoreStructureTerms
Figure 11: The package Symmetric Nets and its built-in sorts and functions
3.3.3 High-level Petri Net Graphs
The complete definition for High-Level Petri Net Graphs is shown in Fig. 12. It extends Symmetric Netsby declarations for sorts and functions and the additional built-in sorts for Integer, String, and List.
21
Terms SymmetricNets
HLPNGs
<<import>>
<<merge>>
<<import>>
<<import>>
<<import>>
<<import>>
<<merge>>
<<import>>
<<import>>
ArbitraryDeclarations
Integers
Strings
Lists
Figure 12: The package HLPNGs
4 XML SyntaxSection 2 and 3 discussed the concepts of the PNML Core Model and the concepts of Place/TransitionNets, High-level Petri Net Graphs, and Symmetric Nets in terms of UML meta-models (and some additionalconstraints). This, however, does not define the concrete XML syntax for representing these concepts.
The XML syntax of the PNML Core Model and the three Petri net types is discussed in this section. ARELAX NG grammar defining the exact XML syntax can also be found at the PNML web site [17].
In Sect. 4.1, we discuss the general format of PNML Documents; i. e. the XML syntax for the PNMLCore Model. In Sect. 4.2, we discuss the format for Place/Transition Nets. In fact, for simple Petri nettypes such as Place/Transition Nets there are some general rules, as to how the concepts of a packagedefining some Petri net type are mapped to XML syntax. This idea is discussed here by the help of theexample of Place/Transition Nets. For High-level Petri Nets, however, there is a dedicated mapping forthe labels of these types to XML. This is discussed in Sect. 4.3.
Note that there is no need for a separate mapping for Symmetric Nets and Place/Transition Nets inHigh-level Notation to XML since, as a restricted version of High-level Petri Nets, these mappings are fullycovered by the mapping for High-level Petri Nets.
4.1 XML syntax of the PNML Core ModelThe mapping of the PNML Core Model concepts to XML syntax is defined for each class of the PNML CoreModel diagram separately.
4.1.1 PNML Elements
Each concrete class2 of the PNML Core Model is mapped to an XML element. The mapping of these classesalong with the attributes and their data types is given in Table 2. These XML elements are the keywordsof PNML and are called PNML elements for short. For each PNML element, the compositions of the PNMLCore Model define in which elements it may occur as a child element.
The data type ID in Table 2 refers to a set of unique identifiers within the PNML Document. The datatype IDRef refers to the set of all identifiers occurring in the document, i. e. they are meant as referencesto identifiers. A reference at some particular position, however, is restricted to objects of a particulartype — as defined by the resp. associations in the PNML Core Model. For instance, the attribute ref of a
2A class in a UML diagram is concrete if its name is not displayed in italics.
22
Table 2: Translation of the PNML Core Model into PNML elementsClass XML element XML Attributes
PetriNetDoc <pnml> xmlns: anyURI(http://www.pnml.org/version-2009/grammar/pnml)
PetriNet <net> id: IDtype: anyURI
Place <place> id: IDTransition <transition> id: IDArc <arc> id: ID
source: IDRef (Node)target: IDRef (Node)
Page <page> id: IDRefPlace <referencePlace> id: ID
ref: IDRef (Place or RefPlace)RefTrans <referenceTransition> id: ID
ref: IDRef (Transition or RefTrans)ToolInfo <toolspecific> tool: string
version: stringGraphics <graphics>Name <name>
reference place must refer to a place or a reference place of the same net. The set to which a reference isrestricted is indicated in the table (e. g. for a reference place, the attribute ref should refer to the id ofa Place or a RefPlace). Note that these requirements are defined in the UML meta-model already; here,these requirements are repeated just for better readability.
Note that the <pnml> element must have a namespace attribute xmlns. For the current version of PNML,this namespace is fixed: http://www.pnml.org/version-2009/grammar/pnml
4.1.2 Labels
Except for names, there are no explicit definitions of PNML elements for labels because the PNML CoreModel does not define other labels. For concrete Petri net types, such as Place/Transition Nets, SymmetricNets, and High-level Petri Nets the corresponding packages define these labels.
In general PNML Documents, any XML element that is not defined in the PNML Core Model (i. e.not occurring in Table 2) is considered as a label of the PNML element in which it occurs. For exam-ple, an <initialMarking> element could be a label of a place, which represents its initial marking, and<inscription>, which represents an arc annotation.
A legal element for a label must contain at least one of the two following elements, which representsthe actual value of the label : a <text> element represents the value of the label as a simple string; the<structure> element can be used for representing the value as an abstract syntax tree in XML.
An optional PNML <graphics> element defines its graphical appearance; and optional PNML<toolspecific> elements may add tool specific information to the label. Note that ISO/IEC 15909-2does not mandate the inner structure of <toolspecific> elements; every tool is free to structure its infor-mation inside that element at its discretion; as long as it produces well-formed XML.
4.1.3 Graphics
All PNML elements and all labels may include graphical information. The internal structure of the PNML<graphics> element, i. e. the legal XML children, depends on the element in which the graphics elementoccurs. Table 3 shows the XML elements which may occur within the <graphics> element (as defined bythe UML model in Fig. 3).
Table 4 explicitly list the attributes for each graphical element defined in Table 3 (cf. Fig. 3 andTable 1). The domain of the attributes refers to the data types of either XML Schema, or CascadingStylesheets 2 (CSS2), or is given by an explicit enumeration of the legal values.
23
Table 3: Possible child elements of the <graphics> elementParent element class Sub-elements of <graphics>
Node, Page <position><dimension><fill><line>
Arc <position> (zero or more)<line>
Annotation <offset><fill><line><font>
Table 4: PNML graphical elementsXML element Attribute Domain
<position> x decimaly decimal
<offset> x decimaly decimal
<dimension> x nonNegativeDecimaly nonNegativeDecimal
<fill> color CSS2-colorimage anyURIgradient-color CSS2-colorgradient-rotation {vertical, horizontal, diagonal}
<line> shape {line, curve}color CSS2-colorwidth nonNegativeDecimalstyle {solid, dash, dot}
<font> family CSS2-font-familystyle CSS2-font-styleweight CSS2-font-weightsize CSS2-font-sizedecoration {underline, overline, line-through}align {left, center, right}rotation decimal
4.1.4 Mapping of XMLSchemaDataTypes concepts
The concepts from the package XMLSchemaDataTypes are mapped to XML syntax in the following way:The String objects are mapped to XML PCDATA, i. e. there will be a PCDATA section within the elementwhich contains the String. This, basically, corresponds to any printable text.
Likewise, Integers, NonNegativeIntegers and PositiveIntegers are mapped to the XMLSchema syntaxconstructs integer, nonNegativeInteger, and positiveInteger, respectively.
4.1.5 Example
In order to illustrate the structure of a PNML Document, there is a simple example PNML Document repre-senting the Petri net shown in Fig. 13, which is a Place/Transition Net. Listing 1 shows the correspondingPNML Document in XML syntax. It is a straightforward translation, where there are labels for the namesof objects, for the initial markings, and for arc annotations.
Note that, in this figure, the initial marking is not displayed as a textual label – it is shown graphically.This is due to the fact that the initial marking comes with a tool specific information on the positions ofthe tokens, tokens are shown at the individual positions as given in the elements <tokenposition>.
Since there is no information on the dimensions in this example (in order to fit the listing to a singlepage), the tool has chosen its default dimensions for the place and the transition.
24
10 20 30 40 50 60
10
20
y
x
ready 2
Figure 13: A simple Place/Transition Net
Listing 1: PNML code of the example net in Fig. 13
<pnml xmlns="http://www.pnml.org/version-2009/grammar/pnml"><net id="n1" type="http://www.pnml.org/version-2009/grammar/ptnet"><page id="top-level"><name>
5 <text>An example P/T-net</text></name><place id="p1">
<graphics><position x="20" y="20"/>
10 </graphics><name>
<text>ready</text><graphics>
<offset x="0" y="-10"/>15 </graphics>
</name><initialMarking>
<text>3</text><toolspecific tool="org.pnml.tool" version="1.0">
20 <tokengraphics><tokenposition x="-2" y="-2" /><tokenposition x="2" y="0" /><tokenposition x="-2" y="2" />
</tokengraphics>25 </toolspecific>
</initialMarking></place><transition id="t1">
<graphics>30 <position x="60" y="20"/>
</graphics></transition><arc id="a1" source="p1" target="t1">
<graphics>35 <position x="30" y="5"/>
<position x="60" y="5"/></graphics><inscription>
<text>2</text>40 <graphics>
<offset x="0" y="5"/></graphics>
</inscription></arc>
45 </page></net>
</pnml>
25
Table 5: Tool specific information for token positionsXML element Attribute Domain
<tokengraphics><tokenposition> x decimal
y decimal
4.2 XML syntax of the Petri net typesBased on the PNML Core Model of Sect. 2.2, Sect. 2.3.1 and 3.3 discussed the definition of some Petri nettypes, which restrict PNML Documents to the particular labels defined in the corresponding packages.
These packages define the labels that are used in the particular Petri net. Here, it is shown how tomap such a package to the corresponding XML syntax. This mapping is the same for all type definitions,unless the type definition explicitly defines a dedicated mapping for this type. This general mapping willbe explained by the help of the example of Place/Transition Nets (see Fig. 5 and the PNML Document inListing 1).
The PT-Net package defines two kinds of labels that can be used in a Place/Transition Net : PTMark-ings and PTAnnotations. Each place can have one annotation PTMarking, and each arc can have oneannotation PTAnnotation. This is indicated by the compositions in the UML diagram in Fig. 5.
The XML syntax for these labels is derived from the role names of these compositions. Every annotationPTMarking is mapped to an XML element <initialMarking>, and every annotation PTAnnotation ismapped to an element <inscription>. Listing 1 shows an example for the XML syntax of a Place/TransitionNet.
Since all labels in this package are annotations, all graphical elements defined for annotations mayoccur as children in these elements.
In the PT-Net package each label is defined to have a <text> element, which defines the actual contentof this annotation. For Place/Transition Nets there are no structured elements.
The corresponding classes from package DataTypes define the XML content of the <text> element.These were discussed in Sect. 4.1.4 already.
Note that for Place/Transition Nets, there is a predefined tool specific extension for the label<initialMarking> (see Sect. 2.3.1), which represents the positions of tokens within a place. The classTokenGraphics is mapped to the XML element <tokengraphics> with no attributes. The token positionscontained by this element are represented by the elements <tokenposition> as shown in Table 5. Withinthe element <tokengraphics> there can be any number of <tokenposition> elements with two attributes xand y.
4.3 Mapping for High-Level Nets
Table 6 defines the mappings between the meta-model elements and their XML representation. In thesetables, only meta-model elements that have corresponding PNML elements or attributes are displayed.Thus, most abstract elements are not shown in the tables, except if they have attributes. All attributetypes are mapped to XMLSchema-datatypes library data types. For details, we refer to the RELAX NGgrammars [17].
5 ConclusionIn this paper, we have outlined the main concepts and the syntax of PNML as defined in ISO/IEC-15909-2,which passed its final ballot and will hopefully be published soon. For lack of space, we could not discussall the details. In particular, we could not discuss the rationale behind the design of PNML and we couldnot discuss all built-in data types and their XML syntax. For the design rationale, we refer to earlierpublications [2, 15, 4] and for some more information on the XML syntax we refer to the PNML web pages[17], which has the full RELAX NG grammar for all currently standardized Petri net types. The ultimatesource of information will be the International Standard ISO/IEC 15909-2.
Another great help for implementing the PNML might be the PNML Framework [18], which providesan API for reading and writing Petri nets in PNML. This API is automatically generated from the PNML
26
Table 6: High-level meta-model elements and their PNML constructsModel element PNML element PNML attributesBooleans::Bool boolBooleans::And andBooleans::Or orBooleans::Not notBooleans::Imply implyBooleans::Equality equalityBooleans::Inequality inequalityBooleans::BooleanConstant booleanconstant value: booleanHLCoreStructure::Declaration declarationHLCoreStructure::Type typeHLCoreStructure::HLMarking hlinitialmarkingHLCoreStructure::Condition conditionHLCoreStructure::HLAnnotation hlinscriptionTerms::Declarations declarationsTerms::VariableDeclaration variabledecl id: ID; name: stringTerms::OperatorDeclaration No element id: ID; name: stringTerms::SortDeclaration No element id: ID; name: stringTerms::Variable variable variabledecl: IDREFTerms::NamedSort namedsortTerms::NamedOperator namedoperatorTerms::Term No elementTerms::Sort No elementTerms::MultisetSort multisetsortTerms::ProductSort productsortTerms::UserSort usersort declaration: IDREFTerms::Tuple tupleTerms::Operator No elementTerms::UserOperator useroperator declaration: IDREFArbitraryDeclarations::ArbitrarySort arbitrarysortArbitraryDeclarations::Unparsed unparsedArbitraryDeclarations::ArbitraryOperator arbitraryoperator
meta-models in the Eclipse Modeling Framework (EMF). More details can be found on the PNML webpages [17].
These web pages are also used for discussing future extensions, some of which might be covered inPart 3 of ISO/IEC 15909. This concerns in particular the precise definition of how to define a Petrinet type (which where used informally only up to now) and its features, and the use this Petri net typedefinition mechanism for defining some more standard Petri types such as timed and stochastic Petri nets.Another major issue is the definition of a module concept for PNML [15, 19, 20]. This setting shouldbe powerful enough to encompass most structuring mechanisms. Hence, it will be possible to exchangemodular and hierarchical models, using different structuring paradigms, between tools so as to apply theirspecific analysis techniques.
If you are interested in some of these issues, you might also want to join the work of WG19 of ISO/IECJTC1 SC7 or the discussion list available at the PNML web pages. All ideas are welcome.
Acknowledgements The work on PNML and ISO/IEC 15909-2 has been going on over 10 years now and manypeople have been involved in the discussion and development process in different stages and different intensity.Since, it is hard to weigh the individual contributions, we thank all of them in alphabetical order: Joao PauloBarros, Jean Bérubé, Jonathan Billington, Didier Buchs, Søren Christensen, Jörg Desel, Erik Fischer, GiulianaFranceschinis, Guillaume Giffo, Jun Ginbayashi, Kees van Hee, Nisse Husberg, Kurt Jensen, Matthias Jüngel,Albert Koelmans, Olaf Kummer, Kjeld Høyer Mortensen, Reinier Post, Wolfgang Reisig, Stefan Roch, KarstenWolf, Christian Stehno, Kimmo Varpaaniemi, Michael Weber, Lisa Wells, Jan Martijn van der Werf, and LukaszZogolowek.
We would also like to thank ISO/IEC for their kind permission to publish this paper based on material of theupcoming standard ISO/IEC 15909.
27
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[16] Stehno, C.: Petri Net Markup Language: Implementation and Application. In Desel, J., Weske, M.,eds.: Promise 2002. Lecture Notes in Informatics P-21., Gesellschaft für Informatik (2002) 18–30
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Recent Publications
[1] van der Aalst, W.M.P.: Process-Aware Information Systems: Lessons to Be Learned from Process Mining. Invan der Aalst, Wil M. P. (Eds.): Transactions on Petri Nets and Other Models of Concurrency II. SpecialIssue on Concurrency in Process-Aware Information Systems, volume 5460 of Lecture Notes in Computer Science,pages 1–26. Springer, 2009. URL: http://dx.doi.org/10.1007/978-3-642-00899-3_1.
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