Advances in Petri Nets 1985

503 Pages·1986·9.199 MB·English

by  B. Baumgarten, H. J. Burkhardt, P. Ochsenschläger (auth.), G. Rozenberg (eds.)

Lecture Notes ni
Computer Science
Edited yb .G Goos and .J Hartmanis
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Editorial Board
D. Barstow W. Brauer .P Brinch Hansen D. Gries D. Luckham
C. Moler A. Pnueli G. Seegmeller .J Stoer N. Wirth
rotidE
G. Rozenberg
Institute of Applied Mathematics and Computer Science
University of Leiden
P.O. Box 9512, 2300 RA Leiden, The Netherlands
CR Subject Classifications (1985): C.1, C.2, D.4, F.1
ISBN 3-540-16480-4 Springer-Verlag Berlin Heidelberg New York Tokyo
ISBN 0-387-16480-4 Springer-Verlag New York Heidelberg Berlin Tokyo
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ECAFERP
This is the second of a series of volumes called "Advances in Petri Nets". ehT
idea of the series originated during the annual "European Workshops on Applications
and Theory of Petri Nets" where the need to present to the general computer science
community recent advances in Petri nets became apparent. yB "recent advances" one
understands here recent results which are the most significant for the development
of the area. ehT workshops are important sources of papers for the "Advances"; the
"best" papers from the past workshops are considered for the series (however, they
og through na independent refereeing process and, if accepted, they often appear in
"Advances" in a quite revised and extended form). Independently of the workshop
papers, "Advances" present also other papers submitted directly for publication in
"Advances" - this is quite evident in the present volume. This development is very wel-
emoc and the potential authors are encouraged to submit papers directly to the
Editor of "Advances".
ehT main aims of "Advances" are:
(I) to present to the "outside" scientific community a fair picture of recent advan-
ces in the area of Petri nets, and
(2) to encourage those interested in applications dna the theory of concurrent sys-
tems to take a closer look at Petri nets and then join the group of researchers work-
ing in this fascinating dna challenging area.
To facilitate (2) above "Advances" will from won on contain also tutorials on
various important topics from Petri nets. ehT current volume presents the tutorial on
synchronic structures written by .U Goltz dna Y, Chong-Yi.
"Advances in Petri Nets 1985" covers the 6th'~European Workshop on Applications
and Theory of Petri Nets" held in Espoo, Finland in June 1985. I would like to thank
K. Jensen, the program committee chairman, for the help in selecting papers from the
workshop to eb submitted for "Advances".
Special thanks og to the referees of papers in this volume ohw very often are
responsible for considerable improvement of papers presented here. The referees were:
A. Andre, P. Azema, D.B. Benson, E. Best, J. Billington, Ph. Chretienne,
.P Chrzastowski-Wachtel, L. Czaja, .R Devillers, .M Diaz, .H Ehrig, F. Feldbrugge,
.H Goeman, .U Goltz, L. Groenewegen, .M Jantzen, K. Jensen, H.C.M. Kleijn, J.W. Klop,
H.-J. Kreowski, .M Latteux, .M Main, A. Mazurkiewicz, .G Memmi, .G eD Michelis,
T. Murata, .M Nielsen, .H Oberquelle, L. Ojala, A. Pagnoni, L. Pomello, .W Reisig,
.G Roucairol, .M Silva, E. Smith, P. Starke, P.S. Thiagarajan, .R Valette, .R Valk,
J. Vautherin, .R ~erraedt, K. Voss, .W Zuberek.
G. Rozenberg
Editor
Leiden, February 1986
ELBAT FO STNETNOC
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
B. Baumgarten, H.J. Burkhardt, P. Ochsenschl~ger, .R Prinoth
The signing of a contract - a tree-structured application . . . . . . . . . . I
.G Berthelot
Checking properties of nets using transformations . . . . . . . . . . . . . . 91
G. Boudol, G. Roucairol, R. de Simone
Petri nets and algebraic calculi of processes . . . . . . . . . . . . . . . . 14
H.-D. Burkhard
Fair controls and their realization . . . . . . . . . . . . . . . . . . . . . 95
L.A. Castellano
Beta processes of C/E systems . . . . . . . . . . . . . . . . . . . . . . . . 83
Y. Chong-Yi
Synchronic distances in C/E systems . . . . . . . . . . . . . . . . . . . . . 101
Y. Chong-Yi
Process periods and system reconstruction . . . . . . . . . . . . . . . . . . 221
G. Comparin, G.A. Lanzarone, K. Lautenbach, A. Pagnoni, .W Panzeri,
A. Torgano
Guidelines on using net analysis techniques wi.th large specifications .... 241
D. Corbeel, J.C.Gentina, C. Vercauter
Application of an extension of Petri. nets to modeli.zation of
control and production processes . . . . . . . . . . . . . . . . . . . . . . 261
L. Czaja
Making nets abstract and structured . . . . . . . . . . . . . . . . . . . . . 181
F. Feldbrugge
Petri net tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
H.J. Genrich
Projections of C/E systems . . . . . . . . . . . . . . . . . . . . . . . . . 224
.U Goltz, Y. Chong-Yi
Synchronic structure - a tutorial . . . . . . . . . . . . . . . . . . . . . . 233
D. Hauschildt, R. Valk
Safe states in banker like resource allocation problems . . . . . . . . . . . 253
A.W. Holt
Coordination technology and Petri nets . . . . . . . . . . . . . . . . . . . 278
K. Jensen, E.M. Schmidt
Pascal semantics by a combination of denotational semantics
and high-level Petri nets . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
Y. Narahari, N. Viswanadham
nO the invariants of coloured Petri nets . . . . . . . . . . . . . . . . . . 330
M. Parigot, E. Pelz
A logical formalism for the study of the finite behaviour of Petri nets . . . 346
H. PIUnnecke
Determination of a poset by its co-relation . . . . . . . . . . . . . . . . . . 362
L. Pomello
Some equivalence notions for concurrent systems. An overview . . . . . . . . 381
.G Richter, K. Voss
Towards a comprehensive office model integrating information
and resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
J. Vautherin
Non-linear invariants for coloured Petri nets with interdependent tokens;
application to the proof of parallel programs . . . . . . . . . . . . . . . . 418
G.R. Wheeler, M.C. Wilbur-Ham, J.Billington, J.A. Gilmour
Protocol analysis using numerical Petri nets . . . . . . . . . . . . . . . . 435
G. Winskel
Petri nets, morphisms and compositionality . . . . . . . . . . . . . . . . . 453
W.M. Zuberek
M-timed Petri nets, priorities, preemptions, and performance
evaluation of systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
The Signin~ ~ a o Contract - a Tree-Structured Application
Modelled with Petri Net Buildin~ Blocks
B.Baumgarten, H.J.Burkhardt
P.Ochsenschl~ger, R.Prinoth
Gesellschaft fur Mathematik und Datenverarbeitung
RheinstraBe 75, D - 6100 Darmstadt
Federal Republic of Germany
Abstract
The desire to replace conventional forms of cooperation within organi-
zational structures by computer services raises the necessity to model
cooperation and to describe it formally.
The complexity inherent to cooperating systems calls for a carefully
structured design facilitating their analysis as well as their imple-
mentation and test.
In this paper we describe an example from the area of human coopera-
tion - namely the negotiation phase of a car purchase financed by a
bank loan. In doing so we exemplify fundamental ideas of modelling and
specifying cooperating systems.
In a first informal analysis, the essential cooperation functions are
identified. In subsequent steps, these functions are assigned to
elements of a model structure which is generally applicable to tree-
structured applications. Using a formally well founded building block
approach, we derive from the problem structure thus obtained a
highly modular net structure. The building blocks as well as their
interrelations are specified by means of product nets, a class of
formally defined high level Petri nets.
The model structure presented in this paper is closely related to the
structure being proposed in ISO's Commitment, Concurrency and Recovery
(CCR) Service, which assures atomic global transactions by correlating
a set of bilateral cooperations.
.i Introduction
In the course of applying the OSI-Reference Model, a concept has to
be agreed upon for modelling distributed applications comprising the
cooperation of n parties n( a )2 and for assembling specific and more
complex distributed applications from basic ones. In /8/, some basic
ideas for such a concept are outlined:
- A distributed application is regarded as cooperation of OSI-
application entities;
- OSI-application entities forming a distributed application may
provide by their cooperation an application service, which is
offered by distinguished application entities within that
application to users outside that application;
users of an application service are again application entities.
-
From an abstract point of view, the cooperation of application
entities guarantees the establishment, progression and release
of global context in a consistent manner /2,3,4,5,6,9/. The users
of such an application expect both the proper coordination of the
activities of the entities involved and freedom from interference
by other activities.
To illustrate the modelling concept for distributed applications
and their application services, in this paper an example taken from
the area of human cooperation is described: the signing of a contract
on a car purchase financed by a bank loan. Due to the overall struc-
ture of the example the application entities are organized in a tree
structure. The substructure of the entities involved derives from the
functionality of the application: Each entity has to handle one or
more bilateral dialogues; it has to come to decisions and possibly it
has to coordinate several dialogues, subject to the global purpose of
the application. One abstraction of these functions leads to the
introduction of building blocks (originally introduced for handshake
patterns /4,6/) as design elements for tree-structured distributed
applications, for which a variety of proof methods were introduced in
/3/. On the one hand, the design process benefits from the structured
and formal approach. On the other hand, due to the reduction of
complexity obtained, the verification of these applications will be
facilitated /6/. Petri nets are particularly suited for the
formalisation of these structures. We used them to describe the
building blocks involved as well as the complete system.
In section 2 the example of signing a contract is described in
terms of natural language. In section 3 an informal model
structure is derived which is in line with ISO's architecture
of CCR /13/. In section 4 the formal model of the example is presented
in terms of Petri nets: The formalization of the functional components
results in the definition of building blocks (special subnets). By
combining these blocks according to the architecture of CCR a complete
net model of the distributed application is constructed. While at
first this is done at the level of a single transaction we turn to
modelling a multitude of concurrent transactions in section .5 Some
formal aspects of the building block approach are treated in the
appendix.
2. Natural language description
A customer who wishes to acquire a car of a certain manufacturer, goes
to a licensed dealer of the manufacturer. The customer informs the
dealer about his personal data, financial situation and the required
model.
The dealer also functions as a loan broker; on behalf of the customer
he applies for a loan with his (the dealer's) bank. The dealer is thus
contractually connected to one bank and one manufacturer. The bank
checks the customer's credit rating. When the check proves positive,
the bank informs the dealer of its approval, otherwise of its refusal.
The manufacturer checks if the required model can be supplied; if
the check proves positive, the dealer is assured of delivery;
otherwise he is informed that delivery is not possible.
When both loan and supply are assured the dealer makes the customer
an offer; otherwise the dealer gives the customer a negative reply.
If bank and manufacturer give one positive and one negative reply
then the dealer responds to the positive reply with a cancellation.
In the case he gets an offer the customer can either accept the offer
by ordering or refuse it. The customer's order is transformed by
the dealer into an order to the bank and another to the manufacturer.
As soon as both orders are confirmed the dealer confirms the order to
the customer.
3. Informal model structure
The very informally described operation of section 2 provides an
example for a distributed application.
On one hand, the customer and the dealer as his contractual partner
form a first application. On the other hand, dealer, bank and
manufacturer constitute by their cooperation a second application
the service of which is represented to the customer by the dealer:
r e m o~ t s u C
/ Dealer
\
!
Fig. 3.1
To become able to describe more than one distinguished car sale,
we base our modelling of this application and its dynamics on roles
which individual participants have to play.
In this course, we introduce and interrelate the following roles:
customer role, dealer role,
bank role, manufacturer role.
In these roles the characteristic behaviour of the participants is
manifested. Within a distinguished car sale these roles are played by
distinguished persons and institutions, e.g.
the customer u, the dealer v,
the bank w, the manufacturer .z
As can be seen from Fig. 3.1 the communications in the distributed
system can be divided into 3 dialogues, corresponding to three role
pairings,
the customer / dealer dialogue,
the dealer / bank dialogue,
the dealer / manufacturer dialogue.
Additionally the role of the dealer must incorporate a coordination of
these role pairings, as indicated in section .2
This necessity of coordination implies that generally the dialogue
related to a role pairing cannot consist of only one question and
one answer. It motivates rather a 2-phase dialogue. A further reason
for the introduction of the 2-phase dialogue is to give the customer
the chance of a refusal even when an offer has been made (after loan
approval and promised delivery).
According to the aforesaid, the dialogue between customer and dealer
can be structured as follows:
- The customer starts the operation with an inquiry to the dealer
(C_INQ_D) .
- The dealer replies with an offer (D_OFF_C) or a refusal (D_NOFF_C).
- In the case of a refusal (D_NOFF_C) the dialogue is terminated;
otherwise the customer continues the dialogue with an order
(C_ORD_D) or a refusal (C_NORD_D).
- In the case of a refusal (C_NORD_D) the operation is terminated;
otherwise the operation is terminated by the dealer's confirmation
of order (D_CON_C).
The structure chosen for the dialogue customer/dealer can also be
transferred to the dialogues dealer/bank and dealer/manufacturer. The
dialogue structure is valid for all 3 cases:
Fig. 3.2