| Peterson, L. J. Petri Net Theory and the Modelling of Systems. Prentice-Hall, Englewood Cli s, NJ, USA, 1981. |
....language called cumulative computing is introduced. Primitive commands become constant specifications, while program compositions become functions on specifications. The notion of resources is not new in computer science. For example, resource at a place in a Petri net represents a local state [14]. In operating systems, the availability of resources can be represented using semaphores [6] Other aspects of resources such as static resource ownership have also been studied in logic [8,13] In this paper, we focus on the cumulation (or dynamics) of resources. In this sense, our approach is ....
....[6] Other aspects of resources such as static resource ownership have also been studied in logic [8,13] In this paper, we focus on the cumulation (or dynamics) of resources. In this sense, our approach is closer to the studies of the dynamic behaviours of real time and reactive processes [4,5,9,11,14]. Indeed they are the typical computational models we intend to study. Our formalism resembles domain theory in many aspects, although the use of volume function is new. It is introduced to simplify the reasoning about limit points and other topological properties. Communicating Sequential ....
Peterson, J. L., "Petri Net Theory and Modelling of Systems," Prentice Hall, 1981.
....for any two given transition rules it is possible to (efficiently) define a new transition rule that has the effect of both. 4. C subsumes the class of finite automata. For example, the above conditions are satisfied by 1 safe Petri nets, general Petri nets, reset Petri nets, transfer Petri nets [Pet81], VASS (vector addition systems with states) BM99] FIFO channel systems [AJ93] etc. However, there are also some classes that not in C. For example, Basic Parallel Processes [Chr93] are not in C, because they are not closed under synchronization (condition 3) Pushdown automata are not in C, ....
J.L. Peterson. Petri Net Theory and the Modelling of Systems. Prentice-Hall, 1981. 25
....[PC graph model by explicitly including communication (send and receive) actors, and setting the execution times of these actors to equal the associated [PC costs. The [PC graph is an instance of Reiter s computation graph model [16] also known as the timed marked graph model in Petri net theory [15], and from the theory of such graphs, it is well known that in the ideal case of unlimited bus bandwidth, the average iteration period for the ASAP execution of an [PC graph is given by the maximum cycle mean (MCM) of Gipc, which is defined by vEC MCM( Gipc) max (3) cycle C in Gip c The ....
J. L. Peterson, Petri Net Theory and Modelling of Systems, Prentice-Hall Inc., Englewoods Cliffs, NJ, 1981.
....the inital population # 0 . This fully describes one simple type of genetic algorithm as a Petri net, in particular a Pr T net. 7. 4 ANALYSING THE GA USING A PETRI NET There are many ways of analysing the Petri net: state analysis, dynamic or static property analysis, and so forth (see e.g. Pet81] In this section we will consider the Petri net given in figure 7.4, which is the simpler version of the model in figure 7.1 with the place P4 omitted both for clarity and because its role is not needed in a simulation of the net (recall that its main advantage is that it closes the token ....
James L. Peterson. Petri Net Theory and the Modelling of Systems. Prentice Hall, Englewood Cliffs, New Jersey, 1981.
....finite disjoint sets) and 0 = the initial state marking of the graph, defined as a function 0 : S . In brief, tokens flow around a net representing events which in circuit terms represents signal changes. One possible method for the analysis of a PN is based upon the matrix view of that net [17]. Using this method a PN is defined by two matrices, D and D , that represent all the output and input functions that are associated with each place in that net. Each matrix will be m rows (for the transitions) by n columns (for the places) and are defined as: i; j] s j ; t i ) where: ....
J. L. Peterson. Petri Net Theory and the Modelling of Systems. Prentice-Hall, 1981.
....1#, 1##010,I1, 1##010,I1, 1##010,I1, 1#, Fig. 3. An Activity Network that is Not Stabilizing Thus the activity network of Figure 3 is not stabilizing. Generally, it is not decidable whether an activity network in a marking 0 is stabilizing. To see this, recall that it can be shown (see [13], for example) that extended Petri nets (Petri nets with inhibitor arcs) are equivalent, computationally, to Turing machines. The proof of this fact is by construction. Specifically, it can be shown that any register machine can be converted into an equivalent extended Petri net. For this reason, ....
J. L. Peterson, Petri Net Theory and the Modelling of Systems, Prentice-Hall, Englewood Cli#s, New Jersey, 1981.
....paths may be followed in a system in parallel. Moreover, some specific nodes of component flowgraphs may correspond to communication statements that depend on one another. In order to capture that it is required to extend the notion of a flowgraph. One possible extension is the Petri net model [16], with a number of tokens representing control flow of component processes as they progress through the system [13] Unfortunately, analysis of a Petri net seems to be more abstract to programmers than the intuitively simpler flowgraph, and requires a great deal of formalism. Another extension is ....
Peterson, J.: Petri Net Theory and the Modelling of Systems. Prentice-Hall, Englewood Cliffs, N.J., 1981.
.... language, nor to any BPP, due to a similar argument as for (e) h) The following BPA with initial state X X a Gamma XA X b Gamma XB X c Gamma A a Gamma B b Gamma generates the language f wcw R : w 2 fa; bg g and hence is not language equivalent to any PN [43]. i) The following PDA with initial state pX pX a Gamma pAX pA a Gamma pAA pB a Gamma pAB qA a Gamma q rA a Gamma r pX b Gamma pBX pA b Gamma pBA pB b Gamma pBB qB b Gamma q rB b Gamma r pX c Gamma qX pA c Gamma qA pB c Gamma qB qX a Gamma q ....
J.L. Peterson (1981). Petri Net Theory and the Modelling of Systems. Prentice-Hall.
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Peterson, L. J. Petri Net Theory and the Modelling of Systems. Prentice-Hall, Englewood Cli s, NJ, USA, 1981.
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J. L. Peterson. Petri Net Theory and the Modelling of Systems. Prentice Hall, 1981.
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J.L. Peterson. Petri-Net Theory and the Modelling of Systems. Prentice-Hall, 1981.
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J.L. Peterson. Petri-Net Theory and the Modelling of Systems. Prentice-Hall, 1981. 16
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J.L. Peterson. Petri-Net Theory and the Modelling of Systems. Prentice-Hall, 1981.
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James L. Peterson 1981. "Petri Net Theory and the Modelling of Systems". Prentice-Hall, Englewood Cliffs, New Jersey.
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Peterson,J.L. (1981) Petri Net Theory and the Modelling of Systems. Prentice-Hall, Englewood Clifs, NJ.
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J. L. Peterson. Petri Net Theory and the Modelling of Systems. Prentice-Hall, 1981.
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J.L. Peterson. Petri Net Theory and the Modelling of Systems. PrenticeHall, 1981.
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J.L. Peterson. Petri Net Theory and the Modelling of Systems. Prentice-Hall, Englewood Cliffs, New Jersey, 1981.
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Peterson, J.L., Petri-net theory and the modelling of systems, Prentice Hall, 1991.
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J. Peterson. Petri Net Theory and the Modelling of Systems. PrenticeHall, 1981.
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J. L. Peterson, Petri Nets Theory and the Modelling of Systems, Prentice-Hall, Englewood Cliffs, NJ, 1981.
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J. Peterson, Petri Net Theory and the Modelling of Systems, Prentice Hall International, Englewood Cliffs, NJ, 1981.
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J. L. Peterson, Petri Net Theory and the Modelling of Systems, Prentice-Hall, 1981.
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Peterson, J.L. (1981). Petri Net Theory and the Modelling of Systems. Prentice Hall.
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Peterson, J.: Petri Net Theory and the Modelling of Systems. Prentice-Hall Inc., 1981.
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