W. Reisig. Petri Nets: An Introduction. Springer-Verlag, New York, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... so, and then generalizes the notion of formal string languages to allow partial ordering rather than just total ordering [16] Mazurkiewicz uses partial orders in developing an algebra of concurrent objects associated with events [14] Partial orders have also been used to analyze Petri nets [17]. Lamport observes that a coordinated notion of time cannot be exactly maintained in distributed systems, and shows that a partial ordering is sufficient [10] 4. Timed concurrent systems A timed system is a tagged system where is totally ordered. That is, for any distinct and in , either or . ....

W. Reisig, Petri Nets: An Introduction, Springer-Verlag (1985).

....a category we mean a diagram in this category given by (v such that (v w) and (v w) is a pullback of (v w) see Figure 1) A Petri net is a model of a concurrent system. Formally, such a net is defined as a bipartite directed graph (cf. Petri 62] Petri 80] Re 85] RT 86] 2.1. Definition. A Petri net, or briefly a net, is a triple N = B; E; F ) where (1) B is a nonempty set of conditions, 2) E is a set of events such that B E = 3) F (B Theta E) E Theta B) is a flow relation such that, for every event e 2 E, the sets F e and eF , ....

Reisig, W., Petri Nets: An Introduction, Springer-Verlag (1985)

....in 1962 [39] Since then, the formal language of PN has been developed and used in many theoretical as well as applicative areas. Introductory survey papers can be found in [37, 3] Several textbooks on the subject are also available: 38] where an extended annotated bibliography is contained) [42, 13, 44]. An yearly Workshop on Application and Theory of Petri Nets is held in Europe (the IX edition of the workshop took place in Venice in June 1988) The classical PNs do not convey any notion of time; in order to use the PN formalism for the quantitative analysis of the performance and ....

W. Reisig. Petri nets - An introduction. Springer-Verlag, 1982.

....2. 1 Basic Petri net theory To provide a complete presentation of the Trellis hypertext model, we reviewfi rst the basic points from Petri net theory that are used in the laterdefi, Readers who desire a more thorough exposition of net theory can consult the texts byPeterson [23] and Reisig [24]. The notation used here is taken from Reisig. Petri net structure A Petri net structure is a triple, N = S#T#F in which S = fs 1 #: # s n g is afi nite set of places with n 0, T = ft 1 #: # t m g is afi nite set of transitions with m 0, and S T = #, F (S Theta T ) T Theta ....

Reisig, W. Petri Nets: An Introduction. Springer-Verlag, 1985.

....and control flow is represented by edges. In fact, almost all WtMS products provide means for graphical specifications similar to state transition nets. Considering only net based methods with a formal foundation, we have to restrict ourselves more or less to statecharts [6] and Petri nets [3] [15]. Variants of Petri nets, especially predicate transition nets, are used in a number of research prototypes as well as in several WtMS products [2] 14] Some workflow management systems use variants of Petri nets for the internal representation of the workflow engine, e.g. 16] Statecharts ....

Reisig, W., Petri Nets: An Introduction, Springer, 1985

....and precede another in a process. SDL [13] and Business Modeling Language (BML) 2, 14] are examples of communication oriented languages that focus on the interaction between people and systems, and between systems. The basic grammar of most process modelling languages derives from Petri nets [15], which provide both a graphical description and formal definition of processes. Researchers [16, 10] have mapped EPC and Task Structures to Petri nets to give the languages formal semantics, and hence to verify the correctness (soundness) of the process definitions. This approach could be used to ....

Reisig, W.: Petri Nets: an introduction. Springer-Verlag, Berlin (1985)

....3 such relation is in general impossible, however. Instead, one generally relies on stronger independence relation deduced from structural properties of the system [GP93] A structural approximation of the independence relation for Petri nets is the following: t 1 o s t 2 iff t 1 t 2 = [Rei85]. The Petri net represented in Figure 2 will be used to illustrate the exploration algorithms proposed in this paper. It exhibits parallelism with t 3 and t 4 , conflict with t 0 #t 1 and t 5 #t 6 , and confusion [Rei85] with t 0 and t 1 . 2.2 State space derivation Table 1 gives a state space ....

....relation for Petri nets is the following: t 1 o s t 2 iff t 1 t 2 = Rei85] The Petri net represented in Figure 2 will be used to illustrate the exploration algorithms proposed in this paper. It exhibits parallelism with t 3 and t 4 , conflict with t 0 #t 1 and t 5 #t 6 , and confusion [Rei85] with t 0 and t 1 . 2.2 State space derivation Table 1 gives a state space derivation algorithm. It is similar to a breadth first standard exploration algorithm. Queue is a stack allowing to store the states to be explored. G represents the set of labeled transitions and H is the set of explored ....

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W. Reisig. Petri Nets : an Introduction. Springer-Verlag,EATCS, 1985.

....is a prerequisite to apply Partial Order techniques. Computing the weakest such relation is in general impossible, however. Instead, one generally relies on stronger independence relation deduced from structural properties of the system [GP93] A version adequate for Petri nets is the following [Rei85]: t 1 o s t 2 i t 1 t 2 = The Petri Net represented Figure 2 will be used to illustrate the exploration algorithms proposed in the paper. It exhibits parallelism with t 3 and t 4 , con ict with t 5 and t 6 , and confusion [Rei85] with t 0 and t 1 . It admits 60 states and 160 ....

....A version adequate for Petri nets is the following [Rei85] t 1 o s t 2 i t 1 t 2 = The Petri Net represented Figure 2 will be used to illustrate the exploration algorithms proposed in the paper. It exhibits parallelism with t 3 and t 4 , con ict with t 5 and t 6 , and confusion [Rei85] with t 0 and t 1 . It admits 60 states and 160 transitions, and includes 4 deadlocks. t1 p2 p6 p7 Fig. 2. Example Petri net 2.2 Persistent sets Persistent sets are particular stubborn sets [Val88a] in which all transitions are enabled. Standard persistent sets exploration preserves ....

W. Reisig. Petri Nets : an Introduction. Springer-Verlag,EATCS, 1985.

....subset of proposed methods, concentrating on those that are, in our opinion, i) sufficiently formal to yield direct implementations, full computerized simulation or rapid prototypes, and (ii) seem to be representative of particularly interesting approaches to the problem. Petri nets (see, e.g. [25]) might be considered one of the best known and bestunderstood solutions. They are graphical and precise, and come complete with an impressive body of research, accumulated over a period of more than 20 years. They are heavily event driven and, by their very definition, allow for maximum ....

W. Reisig, Petri Nets: An Introduction (Springer, Berlin, 1985).

....Cependant il est g en eralement impossible de calculer la relation d ind ependance exacte. Par contre, une approximation peut etre d eduite de la structure du syst eme [GP93] Ainsi pour les r eseaux de Petri place transition une approximation de la relation d ind ependance est donn ee dans [Rei85]: t 1 o s t 2 ssi t 1 t 2 = Le r eseau de Petri repr esent e par la Figure 2 sera utilis e pour illustrer les algorithmes d exploration propos es dans ce papier. Il propose du parall elisme avec t 3 et t 4 , du conflit avec t 5 et t 6 , et le cas de confusion [Rei85] avec t 0 et t 1 . ....

....est donn ee dans [Rei85] t 1 o s t 2 ssi t 1 t 2 = Le r eseau de Petri repr esent e par la Figure 2 sera utilis e pour illustrer les algorithmes d exploration propos es dans ce papier. Il propose du parall elisme avec t 3 et t 4 , du conflit avec t 5 et t 6 , et le cas de confusion [Rei85] avec t 0 et t 1 . Son graphe d etats exhaustif comporte 60 etats et 160 transitions avec 4 blocages. t1 p2 p6 p7 Fig. 2. Exemple de R eseau de Petri 2.2 Ensembles persistans Les ensembles persistans sont un cas particulier des ensembles stubborns [Val88a] dans lesquels toutes les ....

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W. Reisig. Petri Nets : an Introduction. Springer-Verlag,EATCS, 1985.

....to empirical observations. This work demonstrates, that distributed simulation (on a real multiprocessor system) can in fact gain speedup over the sequential simulation this can be achieved even for very small scale TTPNs (reader writer) Introduction 1. 1 Motivation Petri nets (PNs) Pete 77, Reis 85a, Mura 89] are widely recognized to be a good modelling tool for the qualitative study of asynchronous concurrent systems due to their combination of a terse graphic representation and a solid mathematic background. Several timed extensions of the basic Petri net model have been recently proposed ....

W. Reisig. Petri Nets: an Introduction. Springer Verlag, 1985.

....routings. The rest of the section defines the notion of algebraic LES for the net, and introduces the G RUN LES as a canonical example of algebraic LES for the subsequent analysis. In what follows, we assume that the reader is familiar with the basic results of Petri net structural analysis [12]. CD RAS and their Petri net modeling The CD RAS is defined by a set of resource types R R i , i = 1, m , and a set of process types J J j , j = 1, n . Every resource type R i is further characterized by its capacity C i , where is the set of positive integers. ....

....allocation requirement, expressed by an m dimensional vector (a ip ) where a ip 0 #Z , i = 1, m, indicates how many units of resource R i are required to support the stage execution. The resource allocation dynamics taking place in CD RAS can be modeled by a marked Petri net [12]. Specifically, the process flow of each process type J j is represented by a net structure known as Simple Sequential Process (S P ) 10] This net is formally defined by an ordinary strongly connected state machine j = PS j , T j , W j ) such that (i) PS j #= #, p0 j PS j , and ....

W. Reisig, Petri nets : An introduction, Springer-Verlag, 1985.

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W. Reisig. Petri Nets: An Introduction. Springer-Verlag, New York, 1985.

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W. Reisig (1985), Petri Nets: An Introduction. EATCS Monographs on Theoretical Computer Science, Springer.

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W. Reisig. Petri Nets: An Introduction. EATCS Monographs. Springer, 1985.

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Reisig, W., Petri Nets: an Introduction. Springer Verlag, Berlin (1985).

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W. Reisig, "Petri Nets: An Introduction", Springer-Verlag, 1985.

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Reisig, W. (1985) Petri Nets: An Introduction. EATCS Monographs on Theoretical Computer Science, 4. Springer, Berlin.

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W. Reisig. Petri Nets: An Introduction. EATCS Monographs. Springer, 1985.

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Reisig, W., Petri Nets: an Introduction. Springer Verlag, Berlin (1985).

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Reisig W.: Petri nets -- An introduction. EATCS Monographs on Theoret. Comput. Sci., Springer(1985

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Reisig, W.: Petri Nets - An Introduction. Berlin (1985)

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W. Reisig (1985), Petri Nets: An Introduction. EATCS Monographs on Theoretical Computer Science, Springer.

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W. Reisig. Petri Nets: An Introduction. Springer, 1985.

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Reisig, W., Petri Nets: An Introduction. Springer, New York, 1985.

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