K. Jensen. Coloured Petri Nets, Basic Concepts, Analysis Methods and Practical Use., volume 1 of EATCS monographs on theoretical computer science. SpringerVerlag, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....into other places. This is determined by arcs that are directed from places to transitions and from transitions to places. It is assumed throughout this text that the reader is familiar with Petri nets in general as well as coloured Petri nets. Reisig [12] gives a general introduction, Jensen [6] describes coloured Petri nets. Generally speaking, coloured Petri nets permit a more compact representation while o ering the same computational power compared to simpler net formalisms. Reference nets [10] are so called higher (coloured) Petri nets, a graphical notation that is especially well ....

K. Jensen. Coloured Petri nets, Basic Methods, Analysis Methods and Practical Use, volume 1 of EATCS Monographs on Theoretical Computer Science. SpringerVerlag, 1992.

....takes about 318 (460) s for the closed (open) model, which reveals that RG(PN) is strongly connected and M 0 is a home state, once RS(PN) has been explored. 7 Extension towards colored Petri nets We assume that the reader is familiar with colored PNs (CPNs) and the related basic concepts [26]. We first consider CPNs where firing modes (colors) of transitions are explicitly enumerated, such that a static unfolding is straightforward. Definition 7.1 A colored Petri net is a 7 tuple CPN = P; T; C; I Gamma ; I ; G; M 0 ) where P is a finite and non empty set of places, T is a ....

....i and G(t) c t ; M i ) true 0 otherwise R i l = P t2X R i t;c t where X T i nTSC denotes the subset of transitions local to i where G(t) c t ; M) G(t) c t ; M i ) i.e. the guard of t 2 X depends only on M i . If color sets of transitions in a CPN are implicitly given as in [26], the firing mode of a transition results from the bindings of variables assigned to adjacent arcs in the CPN. In that case one can follow the approach described by Christensen and Petrucchi in [14] for modular CPNs which are composed by transition fusion. For a structured representation one needs ....

K. Jensen. Coloured Petri Nets, Basic Concepts, volume 1 of EATCS Monographs on Theoretical Computer Science. Springer, Berlin Heidelberg, 1992.

....nets are a so called high level variant of Petri nets. The reader is assumed to be familiar with appearance and dynamic aspects of Petri nets. This subsection only explains the di erences between the relatively new formalism of reference nets and other high level nets like colored Petri nets [Jen92] Detailed information on Petri nets can be found in [Rei85] while reference nets are described in [Kum98,Kum99] Basically, reference nets look like other Petri nets, but they o er two important additional features: communication by means of synchronous channels and net instances together with ....

K. Jensen. Coloured Petri nets, Basic Methods, Analysis Methods and Practical Use, volume 1 of EATCS monographs on theoretical computer science. Springer-Verlag, 1992.

....of the system. During graph generation, we need to decide repeatedly whether for a (recently generated) state an equivalent one has been explored earlier. In the context of high level Petri nets, we can use operations and relations of the color sets to describe the symmetries symbolically [HJJJ84, Jen92]. Then the user can provide the description of the symmetries together with the system. For some classes of high level nets, the description can be deduced automatically [CDFH90, Jun98] though this approach seems to be rather sensitive to the syntax used for the net description. Furthermore it is ....

K. Jensen. Coloured Petri Nets, volume 1 of EATCS Monographs on Theoretical Computer Science. Springer, 1992.

....and values, often called colours in Petri net literature. In addition, each place in the net al..so has a type, restricting the type of tokens allowed in that place. When firing a transition, the number of tokens produced and their value may be determined by the value of the consumed tokens. See [7, 8] for a detailed treatment of the theory of coloured Petri nets. The traffic light example shows simple use of data in Petri nets. It is no longer necessary to have separate places for each colour that a traffic light may have. Instead, the colour can be stored in the tokens in the net. In ....

....It appears that the translation proposed in this paper can be automated without too many difficulties. Coloured invariants. An interesting extension to ExSpect would be, the use of colours, or data, in invariants. Place and transition invariants as explained in Section 3 cannot handle data. In [8], invariants are generalized to coloured nets. Design CPN [6] is a tool that implements coloured invariants. A disadvantage of coloured invariants is that it is no longer possible to calculate all invariants using linear algebra. It is only possible to verify whether a specification satisfies a ....

K. Jensen. Coloured Petri Nets. Basic Consepts, Analysis Methods and Practical Use, volume 28 of EATCS monographs on Theoretical Computer Science. Springer--Verlag, Berlin, Germany, 1992.

....nets [31] extend this state transition setting by allowing states to be distributed across different locations. These formalisms must be extended with facilities for specifying data types in specification languages such as e.g. LOTOS [16, 3] OCCAM [15] and colored and algebraic Petri nets [17, 32] to allow more complex data structures in the systems. Executable specifications of reactive systems may be interpreted (and thus executed) in various ways, e.g. following all possible execution traces, simulating one run, etc. The operational choice of execution model is usually either embedded ....

K. Jensen. Coloured Petri Nets, Basic Concepts, Analysis Methods and Practical Use, volume 1 of EATCS Monographs on Theoretical Computer Science. Springer-Verlag, 1992.

....prototypes very quickly. Acknowledgments We wish to thank Robert Riemann for his critical comments on an earlier version of this paper. We also benefited from numerous discussions with Frank Wallner and Ahmed Bouajjani. A The M net model M nets [6] are a class of traditional high level Petri nets [22] with a generalized inscription of places, transitions and arcs: inscription = label, annotation) The annotation drives the vertical unfolding of a M net into a classical P T nets. Moreover, the M net model is equipped by an algebra which allows to compose smaller M nets to more complex ones. ....

Kurt Jensen. Coloured Petri Nets. Basic Concepts, Analysis Methods and Practical Use, volume 1 of EATCS Monographs on Theoretical Computer Science. Springer, 1992.

....i A i t1 t2 t3 t4 pending with quiet uninformed accepted terminated waiting mailbox pending = pr1(pending with) Figure 4: Petri net Sigma: the echo algorithm concise definition of high level Petri nets is given in the appendix. The mathematical theory of high level Petri nets can be found in [6]. 2.2 Properties of the echo algorithm Now, we will formalize the essential properties of the echo algorithm, which will be verified in Sect. 4. Again, we introduce our formalism in an informal way. As usual, we distinguish safety and liveness properties. The first property states that the ....

K. Jensen. Coloured Petri Nets, Volume 1 of EATCS Monographs on Theoretical Computer Science. Springer-Verlag, 1992.

....believe that it can be similarly applied to other important classes of nets that we cannot discuss in detail due to space limitations. We brie y address how similar representations could be de ned for other Petri net classes, such as colored Petri nets based on (higher order) programming languages [39], nets with macroplaces [2, 3] nets with FIFO places [30, 40, 29, 27] object oriented variants of Petri nets [68, 44] and object nets [73, 74, 28, 75] where nets are viewed as token objects. We conclude this introduction with a brief overview of the paper: After introducing rewriting logic ....

.... In this paper we subsume such approaches under the general notion of algebraic net speci cations, parameterized over an underlying equational 7 In fact, the nets introduced in [38] are called colored Petri nets (CPNs) but this name has later been used for the more syntactic version introduced in [39], which is also the sense for which we would like to reserve this term (see below) speci cation language. The main feature that algebraic net speci cations have in common with predicate transition nets is that an algebraic net speci cation does not necessarily specify a single colored net, but ....

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K. Jensen. Coloured Petri Nets, Basic Concepts, Analysis Methods and Practical Use., volume 1 of EATCS monographs on theoretical computer science. SpringerVerlag, 1992.

....algebra algebraic semantics abstraction verification top down design 1 Introduction Motivation. The theory of Petri nets (see for example [31] has been developed to design and analyze distributed systems. In order to support the design of large, complex systems, high level Petri nets [21, 23] have been defined, which include hierarchy, data, and time. Based on high level Petri nets, automated tools, such as Design CPN [26] and ExSpect [1] have been developed. The most important reasons for the widespread use of Petri nets in the area of system design, are their intuitive graphical ....

....hierarchical net can also contain subnets, whose pins are connected to internal places or pins from the high level net. Essentially, this is the hierarchy construct underlying the high level nets described in [21] It is also one of the constructs used to build hierarchical nets as described in [23]. Furthermore, it is supported by tools as Design CPN and ExSpect. The main objective of this paper is to give an algebraic semantics for the observable behavior of hierarchical nets, that is, their behavior projected onto pins. Therefore, it seems most appropriate to define the behavior of a net ....

K. Jensen. Coloured Petri Nets. Basic Concepts, Analysis Methods and Practical Use, volume 1, Basic Concepts, volume 28 of EATCS monographs on Theoretical Computer Science. Springer--Verlag, Berlin, Germany, 1992.

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