User:Steve.hostettler
| This is a Wikipedia user page. This is not an encyclopedia article or the talk page for an encyclopedia article. If you find this page on any site other than Wikipedia, you are viewing a mirror site. Be aware that the page may be outdated and that the user whom this page is about may have no personal affiliation with any site other than Wikipedia. The original page is located at https://en.wikipedia.org/wiki/User:Steve.hostettler. |
Algebraic Petri Net is an evolution of the well known Petri net in which instances of User Defined Data Types called Algebraic Abstract Data Types (AADT) replace black tokens. This formalism can be compared to Coloured Petri Nets[1] in many aspect, however the
semantic of the data types is given by an axiomatization enabling proofs and computations on it.
Algebraic Petri Nets[2] where invented by Jacques Vautherin in 85 in is PhD thesis and later reworked by Wolfang Reisig[3].
The following picture describes an Algebraic Petri Net model of the Dining Philosopher problem. It contains two parts, the left one (the control) is a Petri Net while the right one (the data part) is modeled using AADT.
There are two AADT in this model, one for the fork algebra, one for the philosopher algebra. Please note that the philosopher AADT used the fork one.Since all the philosopher can take their left fork without the right one, this model result in a deadlock.
The control part is composed of :
- Places contain multisets (bags) of tokens. Those tokens are instances of AADT (in this case terms that represent either a philosopher or a fork).
- Arcs can be labelled with multisets of free terms. Terms are built from the signature given in the AADT.
- Transitions are events that can be fired whenever there is enough resources (there is enough tokens in the input places to satisfy all the input arcs) and the guard (condition) of the transition holds. Then the produced tokens are put in the target places of the output arcs.
References
- ^ K. Jensen. Coloured Petri Nets. Springer, Berlin, 1996.
- ^ Jacques Vautherin: Parallel systems specifications with coloured Petri nets and algebraic specifications. European Workshop on Applications and Theory of Petri Nets 1986: 293-308
- ^ Wolfgang Reisig: Petri Nets and Algebraic Specifications. Theor. Comput. Sci. 80(1): 1-34 (1991)
Further reading
- Vautherin, Jacques (85). Un Modele Algebrique, Base sur les Reseaux de Petri, pour l'Etude des Systemes Paralleles. These de Docteur Ingenieur, Univ. de Paris-Sud, Centre d'Orsay.
{{cite book}}: Check date values in:|year=(help)CS1 maint: year (link) - Jensen, Kurt. Coloured Petri Nets. Springer Verlag. ISBN 3-540-62867-3.