Applications and Theory of Petri Nets: Selected Papers from the 3rd European Workshop on Applications and Theory of Petri Nets Varenna, Italy, September 27–30, 1982 (under auspices of AFCET, AICA, GI, and EATCS)

322 Pages·1983·16.24 MB·English

by  C. A. Petri (auth.)

Informatik - Fachberichte
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gegeben von R. Gnatz und K. Samelson. VIII, 327 Seiten. 1977. 1980
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Informatik-Fachberichte
Herausgegeben von W. Brauer
im Auftrag der Gesellschaft für Informatik (GI)
66
Applications and Theoi)'
of Petri Nets
Selected Papers from the 3rd European Workshop
on Applications and Theory of Petri Nets
Varenna, Italy, September 27-30, 1982
(under auspices of AFCET, AICA, GI,
and EATCS)
Edited by
Anastasia Pagnoni and Grzegorz Rozenberg
Springer-Verlag
Berlin Heidelberg New York Tokyo 1983
Herausgeber
Grzegorz Rozenberg
Institut of Applied Mathematics and Computer Science
University of Leiden, Wassenaarseweg 80, P.O. Box 9512
2300 RA Leiden, The Netherlands
Anastasia Pagnoni
Istituto di Metodi Quantitativi, Universita "Luigi Bocconi"
Via Sarfatti, 25 - 20136 Milano, Italy
CR Subject Classifications (1982): 4.29,4.39,4.6, 5.23, 5.29, 5.9, 3.89
ISBN-13: 978-3-540-12309-5 e-ISBN-13: 978-3-642-69028-0
001: 10.1007/978-3-642-69028-0
Library of Congress Cataloging in Publication Data. European Workshop on Application
and Theory of Petri Nets (3rd: 1982: Varenna, Italy) Applications and theory of
Petri nets. (Informatik-Fachberichte; 66) 1. Petri nets--Congresses. 2. MachIne
theory--Congresses. I. Pagnoni, Anastasia. 11. Rozenberg, Grzegorz. 111. Tille. IV. Series
QA267.E97 1982 511 83-6632
ISBN-13: 978-3-540-12309-5 (U.S.)
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lor other than private use, a lee is payable to "Verwertungsgesellschaft Wort", Munieh.
© by Springer-Verlag Bertin Heidelberg 1983
111
Preface
This volume presents a selection of papers presented at the 3rd European Workshop on
Appl ications and Theory of Petri Nets that took place in Villa Monastero, Varenna
(Italy) in the period September 27 - September 30, 1982.
The I ist of topics included:
nets and related models, mathematical analysis of nets, transformations and morphisms
of nets, formal languages and nets, parallel program verification and nets, the pro
blem of time in nets, programming languages based on nets, applications to distributed
systems, applications to realtime systems, software ~~gineering, hardware design and
its implementation, recoverability problems, nets and formal semantics; net tools.
The diversity of topics on this list witnesses the fact that the researchers from very
different areas presented their contributions and discussed various research problems
during the workshop. This interaction of scientists looking at the area of Petri nets
from very different points of view makes this series of workshops interesting and
worthwi le.
The volume documents the progress of the research concerning Petri nets during a one
year time from the 2nd European Workshop held in Bad Honnef in 1981.
We think that this was a substantial progress indeed.
This observation is even more pleasant if one real izes that during the workshop in
Varenna we have celebrated 20 years of "existence" of Petri nets (the seminal work
by prof. C.A. Petri appeared precisely 20 years ago). We are very proud to present an
invited address by prof. C.A. Petri in this volume.
The workshop was sponsored by the following institutions:
- CNR (Ital ian Research Council)
- FAST (Federazione Associazioni Scientifiche e Tecniche)
- Istituto di Cibernetica (University of Milan)
- Ente Villa Monastero
We are very grateful for this support.
The aim of this workshop was to present the latest contributions in, and to stimulate
further research on the theory and appl ications of Petri nets.
We are convinced that this aim has been achieved and hence the workshop was succesful.
We are very grateful to al I the participants of the workshop for turning it into a
meeting of very useful scientific and very pleasant personal contacts. We al I look
forward to (at least) other 20 years of successful development of the theory and of
the appl ications of Petri nets.
A. Pagnoni
G. Rozenberg
v
Table of contents
Preface 111
1nvited address
Some personal views of net theory
C.A. Petri 1
List of contributions
Structural transformations giving B-equivalent PT-nets
C. Andre 14
Equivalence notions for concurrent systems
F. Oe Cindio, G. Oe Michelis, L. Pomello, C. Simone 29
Milner's communicating systems and Petri nets
F. Oe Cindio, G. Oe Michelis, L. Pomello, C. Simone 40
A matrix-based implementation of generalized Petri nets
M. Courvoisier 60
Petri nets specification of virtual ring protocols
P. Estaillier, C. Girault 74
A note on O-continuous causal nets
c. Fernändez, P.S. Thiagarajan 86
S-invariance in predicate/transition nets
H.J. Genrich, K. Lautenbach 98
A diagram editor for line drawings with inscriptions
H.J. Genrich, R.M. Shapiro 112
Formal semantics by a combination of denotational semantics and high-level
Petri nets
N.O. Hansen, K.H. Madsen 132
Notions of computability by Petri nets
M. Jantzen, H. Bramhoff 149
VI
High-level Petri nets
K. Jensen 166
Specification and verificatio!1 of networks in a Petri net based language
t~. Kyng 181
Construction of distributed systems from cycle-free finite automata
R. Prinoth 199
A graph theoretical property for minimal deadlocks
G. Memmi 221
Petri nets with individual tokens
W. Reisig 229
Subset languages of Petri nets
G. Rozenberg, R. Verraedt 250
Control of flexible production systems and Petri nets
R. Valette, t1. Courvoisier, D. t1ayeux 264
On the notion of interface in condition/event-systems
K. Voss 278
Behavioral equivalence of concurrent systems
M. Yoeli, T. Etzion 292
Program of the workshop 306
Addresses of contributors 310
SOME PERSONAL VIEWS OF NET THEORY
C.A. Petri
Gesellschaft für Mathematik
und Datenverarbeitung m.b.H.
Schloss Birlinghoven
D-SZOS St Augustin 1
Twenty years have passed since the first publication on net theory.
I am grateful for the opportunity to speak on a topic of my choice on
this occasion.
What comes first to my mind is that the net theory of today is the work
of many people. A historical review would have to start with the encour
aging constructive criticism of the late Alwin Walther, whose far-sighted
remarks on my eccentric proposals are still governing my research; it
would continue with the early, and timely, contributions of Anatol Holt
and of Hartmann Genrich, who have deeply influenced the way we think
about nets today; I feel that it is not possible for me to give due
acknowledgement to the numerous further contributors, even by such short
characterisations, within a reasonable time. For the same reason, I shall
not attempt to give an overview of published results. Nor shall I misuse
this occasion to smuggle in unrefereed new material.
Rather, I shall direct your attention to the future. Needless to say :
one of the tasks at hand is to consolidate net theory as a mathematical
theory, and to supplement that mathematical theory with a manual on the
methodology of its application.
A Difficulty
The mathematicians among us tend to feel confident about their own part
of the task, realistically expecting that it will take many years to be
accomplished. Let me add another year to the span of these expectations,
also adding another hope (to some: a horror) by pointing out the possi
bility to look at net theory as at a generalization of set theory, not
only as an intra-mathematical application of set theory. One might say
that the "strict firing rule" for condition/event nets is - at the level
of foundations of mathematics - a matter of carrying over the Extension
ality Principle for classes and sets, to the basic concept of change :
2
just as two sets are defined to be equal iff they comprise the same
elements, i.e. iff they have the same "extension" so let two changes
be called equal iff they comprise the same items of the form "x E y be
comes valid" resp. " ... ceases to be valid"; i.e. let changes also be
fully characterized by their extension. - The new (1979) approach to
mathematically modelling the indispensable idea of continuous change
(e.g. motion) as applied to real-world systems is not based on the ab
stract "real"-number system, but rather on the notion that the idea of
"change" should be firmly anchored in the very foundations of mathema
tics; at least to this extent let computer science have an influence on
meta-mathematics (and vice versa) .
Three Topics for Future Research
Even if you cannot share the viewpoint of the previous paragraph, I ex
pect you will admit, without Gödel's proof, that the abstract study of
nets is limitless. Net theory must find it goals and signposts outside
of its mathematics. It is therefore obvious that any rational choice of
specific research topics must refer to real-world affairs, and must re
flect a personal judgement on importance and on feasibility.
I select three topics for future application of net theory
~ Formal Pragmaties (FP)
Net Theory Computer-Aided-Design Tools (CAD)
Physics/basic Technologies (PT)
and shall trace them to their origins in the beginnings of net theory,
as published twenty years ago.
Let me admit at once I am aware that I cannot attain completeness of
my exposition in any point of detail, nor do I expect a completion of
the proposed studies in a near future. Also, successful research seems
not feasible if performed by a small group of persons; so what I say
here has a component of advertising. Finally, I have to admit that, in
spite of the amount of work al ready done in preparation, the projected
research activities are still of high difficulty and not without risk.
On the other hand, they are not without promise of a rich pay-off, and
not chosen without an attempt of systematic procedure: In Table 1,
taken from (~J p. 11, topic (FP) refers to the uppermost levels, topic
(CAD) to the medium levels, and topic (PT) to the formally weIl re
searched five lowest levels. (Level k is reached from level k - 1 by
applying a net morphism).
3
Level number: Typical concepts:
n: Interests Restrictions
(of groups,individuals •.• ) (natural,legal,economic ••• )
n-1 : Channels Agencies
(for resources,messages ... ) (institutions,offices ..• )
Roles Activities
(of people,artefacts ••• ) (belonging to each role)
n-2: Global reliability Performance
n-3: Oata bases Computer architectures
Protocols Operating systems
~u
r::
..~...
Files Tasks u
Cf)
Records Statements .!.-<,
~
;:l
Machine words Machine instructions Pso
0
u
if, and, assignment, identifier, value .. ,
NANO-gates, delays, clocks ...
4 :
transistors diodes oscillators
3 : "Stations", "flux" , "Transfers", "influence"
(as used in low level information flow graphs)
2 : Conditions Transitions
Synchrony "Enlogy"
(as used in condition-event systems and
transition nets)
1 : Occurrences and their partial order in time
(Occurrence nets)
0: Concurrency structures ("ropes")
Table 1: A sequence of conceptual levels concerning
computer science, its foundations and certain applications
4
Formal Pragmatics
Semiotics is the science of communicating by messages which are (com
posed of) signs or symbols. It is commonly subdivided into syntactics,
semantics, and pragmatics. Especially through the influence of computer
science, we have today quite satisfactory formalizations for syntactics,
i.e. for the composition of messages, and just satisfactory formaliza
tions of semantics, i .e. for the analysis of the meaning of messages.
There have been many attempts to formalize the effects of messages upon
a recipient: that is the narrower sense of "pragmatics" as originally
defined. In the context of computer languages, this is just what formal
semantics does; a standard recipient is assumed, and "he" is (or may be)
defined in terms of how he reacts to standardized messages.
Outside of computing, typical attempts to formalize pragmatics have con
sisted in building a theory about a relation such as "the (human) reci
pient X accepts (believes in) the assertive message M at time t".
This is, of course, a still more restricted view of pragmatics than the
original one. For my own part, I choose to consider pragmatics as the
entire rest of semiotics which remains when we sub_.tract syntactics and
the recipient-independent part of semantics (in case it should exist).
How can one hope to cover an area of such stupendous size and complexity?
1. By concentrating on practical problems of acknowledged importance,
e.g. on avoiding high-level malfunctions in computer-based communi
cation.
2. By proceeding cautiously and modestly step by small step.
3. By employing formal approaches and means whose suitability for the
purpose has been tested and to some extent verified for a long time.
E.g. :
1962: one declared purpose )
Net Theory Formal Pragmatics
>
>1982: development
4. By thinking beyond the purely technical aspects of "data" when
considering messages in a pragmatic context.
Let us acknowledge that in all cases of practical relevance, the handling
of messages affects not only the knowledge of recipients, but also -
more significantly - the rights and duties of all involved agencies,
their interests and abilities, their power and their secrets. their
actions and their expectations.
This enumeration makes obvious some of the definite limits to useful
formalization of pragmatic affairs. No amount of pragmatic analysis of
messages will reveal all of the relations between the agencies within an