Rob van Glabbeek and Frits Vaandrager. Petri net models for algebraic theories of concurrency. In Proceedings of PARLE, Volume 259 of the Lecture Notes in Computer Science, pages 224--242, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....system and running through all four tuples of transitions, the N free property can be algorithmically checked (using polynomial space) 4 Net constructions In this section, we will give constructions on nets which correspond to the expression operations. Many of these are known from earlier work [10, 9, 25, 3, 18]. Examining their properties will tell us which constructions preserve which net subclasses, a synthesis property. We will still have to look at analysis that is, whether all net systems in a particular subclass are de nable using particular kinds of expressions, and we leave this to the next ....

R.J. van Glabbeek, F.W. Vaandrager. Petri net models for algebraic theories of concurrency, Proc. PARLE, Eindhoven (J.W. de Bakker, A.J. Nijman, P.C. Treleaven, eds.), Vol. 2, LNCS 259 (1987) 224-242.

....to the question as to whether it is possible to transform any given Standard Workflow Model to an equivalent Safe Workflow Model. A technique typically required for this is node replication (illustrated in Figure 5. 12) Node replication can be compared to net unfolding as described in for example [GV87]. The unfolded net can be thought of as the safe version of the original net. Unfolding as described in [GV87] preserves bisimulation equivalence. It is immediately clear that if the original net is not bounded, then the unfolding is infinite. Hence, it is impossible to convert a Standard ....

....Workflow Model. A technique typically required for this is node replication (illustrated in Figure 5.12) Node replication can be compared to net unfolding as described in for example [GV87] The unfolded net can be thought of as the safe version of the original net. Unfolding as described in [GV87] preserves bisimulation equivalence. It is immediately clear that if the original net is not bounded, then the unfolding is infinite. Hence, it is impossible to convert a Standard Workflow Model that may Figure 5.12: Node replication result in an unlimited number of multiple instances of some ....

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R.J. van Glabbeek and F.W. Vaandrager. Petri net models for algebraic theories of concurrency (extended abstract). In J.W. de Bakker, A.J. Nijman, and P.C. Treleaven, editors, Proceedings PARLE, Parallel Architectures and Languages Europe, Vol. II: Parallel Languages, volume 259 of Lecture Notes in Computer Science, pages 224 242, Eindhoven, The Netherlands, June 1987. Springer Verlag.

....between the a i and the b j but preserve the concurrency within the b j , and so we do a simple cross product construction on the start places of both nets. We note that this causes all the transitions to be in conflict, as desired. The resulting net is given in Figure 2 7. As discussed in [42], one technical complication arises due to initially marked places that have incoming transitions, and in general, we apply a start unwinding operator on nets before doing the above construction. Our start unwinding operator, illustrated in Figure 2 8, is essentially the same as that of [15, 42] ....

....in [42] one technical complication arises due to initially marked places that have incoming transitions, and in general, we apply a start unwinding operator on nets before doing the above construction. Our start unwinding operator, illustrated in Figure 2 8, is essentially the same as that of [15, 42] and produces a net that is essentially the same as the original net, except that all initially marked places have empty presets. The start unwound net is identical to the original net whenever all initially marked places of the original net have empty presets. Definition 2.2.12 Let hN; ....

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R. van Glabbeek and F. Vaandrager. Petri net models for algebraic theories of concurrency. In Proceedings of PARLE '87, Volume 259 of the Lecture Notes in Computer Science, pages 224--242, 1987.

....other actions the agent can invoke in that intermediate state, a lot of information can be deduced about its concurrent behaviour. In fact, non atomic execution corresponds to what is known in the research area of non interleaving models of behaviour as the ST principle, originally introduced in [24]; this principle gives rise to coarsest congruences for action refinement (see [3, 25, 58] In the absence of auto concurrency, the ST principle comes down to the simple splitting of actions without using keys; see [2] 2.2 Virtual machines Definition 2.5 (virtual machine) A virtual machine ....

....into reality. 5.5 Legacy research and related work This paper could not have been written in the absence of the past decade of research on action refinement. We have already included numerous references in the main text; worthwhile repeating is the debt to the work on ST semantics, introduced in [24] and later proved to give rise to coarsest congruences w.r.t. action refinement in [3, 29] With much the same aim in mind as in the current paper, we previously developed a correctness notion based on vertical implementation in [54] Translated in terms of the current paper, vertical ....

R. J. van Glabbeek and F. W. Vaandrager. Petri Net models for algebraic theories of concurrency. In J. W. de Bakker, A. J. Nijman, and P. C. Treleaven, eds., PARLE --- Parallel Architectures and Languages Europe, Volume II: Parallel Languages, vol. 259 of Lecture Notes in Computer Science, pp. 224--242. Springer-Verlag, 1987.

....bisimilarity [2] and (forward) interface equivalence [21] Weak place bisimilarity [1] allows abstraction from transitions, whereas interface equivalence allows abstraction from places. Event oriented equivalences that satisfy the second requirement are the various bisimilarities. ST bisimilarity [12], 19] also satisfies the third and fourth requirement. Place bisimilarity has a very appealing reduction algorithm. For bounded nets, interleaving bisimilarities share this property, but they require the costly construction of the whole state space of the net. SE bisimilarity does not allow ....

....with weight n from p to t. For O, the arcs are inverted. Weights one are omitted for clarity. 4.1 SE bisimilarity Let L be a net. For convenience, we omit subscripts L. The concept of SE bisimilarity stems from the notion about the dynamic behavior of nets, where actions have a duration, as in [12]. Each action can be started and then committed. Between these events, the action is executed. The fact that actions are not atomic allows one to model concurrency without causality: two actions are concurrent in a given state if one can be started immediately after starting the other, so that ....

R.J. van Glabbeek and F. Vaandrager. Petri Net Models for Algebraic Theories of Concurrency. In J.W. de Bakker, A.J. Nijman, and P.C. Treleaven, editors, PARLE: Parallel Architectures and Languages

.... f; i is a name for a clock with associated distribution f . The name f; i which is used for a starting clock must be such that i is the least i 2 N I which is not used in the name of any clock with the same distribution f already in execution. Note that, similarly as for standard ST models [1,7,11,15], using just duration distributions as clock names is not sucient because indexes i 2 N I are needed in order to uniquely relate the clock termination event to the corresponding clock start event, even in the situation where several clocks with the same duration distribution are simultaneously ....

R.J. van Glabbeek, F.W. Vaandrager, \Petri Net Models for Algebraic Theories of Concurrency", in Proc. of the Conf. on Parallel Architectures and Languages Europe (PARLE '87), LNCS 259:224-242, 1987

....that the main concerns are the introduction and examination of various programming constructs. New constructs are introduced equationally, rather than operationally, and it is not always clear that there is an appropriate and straightforward operational semantics. Some work in this area includes [AB84, BB88, BV89, BvG87, BK82, BK84b, BK84a, BK85, BT86, vGR89, vGV87, dBBKM82, dMOZ86, dBZ83]. The field of true concurrency works from the hypothesis that there is an important difference between parallelism and interleaving. In CCS and related areas, if a and b are atomic actions, then there is no significant differ14 ence between running a and b in parallel and nondeterministically ....

Rob van Glabbeek and Frits Vaandrager. Petri net models of algebraic theories of concurrency. In J. W. de Bakker, A. J. Nijman, and P. C. Treleaven, editors, PARLE: Parallel Architectures and Languages Europe, Volume II, number 259 in Lect. Notes in Computer Sci., pages 224--242. Springer-Verlag, 1987.

....the works of [GV89] and [BD92] by defining truly concurrent behaviors. Namely, we describe truly concurrent models modulo a truly concurrent equivalence. The models we consider are Asynchronous Transition Systems (of [Shi85] and [Bed87] and the behavioral equivalence is ST bisimulation (of [GV87]) Our appraoch has two main advantages : we deal with transition system like models, which is much more easy to understand than other approaches based on Petri nets or event structures, and we do not restrict to a particular specification, but instead we consider a class of specifications. We ....

.... : we find interesting to present its definition over Asynchronous Transition Systems since it is simpler than in [Gla90b] for prime event structures: we do not need to carry along information about the past of the computation (instead, we come closer to the original definition for Petri nets in [GV87]) Moreover, ST bisimulation is known to well behave w.r.t. the refinement of actions (see [Gla90c] for this notion) Refinement is out of the scope of this paper, but will be the subject of an oncoming paper (see [Ech93] Finaly, the decidability of ST bisimulation over finite models (even if ....

[Article contains additional citation context not shown here]

R. J. van Glabbeek and F. Vaandrager. Petri net models for algebraic theories of concurrency. In Proc. PARLE'87, vol. II: Parallel Languages, Eindhoven, LNCS 259, pages 224--242. Springer-Verlag, June 1987.

....other actions the agent can invoke in that intermediate state, a lot of information can be deduced about its concurrent behaviour. In fact, non atomic execution corresponds to what is known in the research area of non interleaving models of behaviour as the ST principle, originally introduced in [24]; this principle gives rise to coarsest congruences for action refinement (see [3, 25, 58] In the absence of auto concurrency, the ST principle comes down to the simple splitting of actions without using keys; see [2] 2.2 Virtual machines Definition 2.5 (virtual machine) A virtual machine is ....

....into reality. 5.5 Legacy research and related work This paper could not have been written in the absence of the past decade of research on action refinement. We have already included numerous references in the main text; worthwhile repeating is the debt to the work on ST semantics, introduced in [24] and later proved to give rise to coarsest congruences w.r.t. action refinement in [3, 29] With much the same aim in mind as in the current paper, we previously developed a correctness notion based on vertical implementation in [54] Translated in terms of the current paper, vertical ....

R. J. van Glabbeek and F. W. Vaandrager. Petri Net models for algebraic theories of concurrency. In J. W. de Bakker, A. J. Nijman, and P. C. Treleaven, eds., PARLE --- Parallel Architectures and Languages Europe, Volume II: Parallel Languages, vol. 259 of Lecture Notes in Computer Science, pp. 224--242. Springer-Verlag, 1987.

.... and the models most often used are transition systems [Plotkin 1981] and equational algebras [Bergstra et al. 1984] Most of this work has been based on interleaving models and only recently have attempts been made to give a truly concurrent semantics to these languages ( Degano et al. 1989] [van Glabbeek et al. 1987], Olderog 1987] An earlier denotational semantics using event structures as domains was given in [Winskel 1982] In this framework, Hennessy and Milner [Hennessy et al. 1985] have used action indexed logics to characterize computations of sequential nondeterministic systems. Assuming an ....

van Glabbeek R, Vaandrager F 1987 Petri net models for algebraic theories of concurrency, LNCS 259:224-242.

....by one step. The observer first toggles the clock and then notes the behaviour on the n lines (which may appear at different times with respect to some real clock) and the process continues. This is shown in figure 1. The semantics developed here is similar to the step semantics developed in [vGV87] but the number of actions in a step is bounded. However as will be seen later, we do not assume a synchronous model. Therefore, our semantics is different from SCCS [Mil83] where asynchronous evolution is disallowed. Not all processors in the system may be required by a process at all the ....

R. J. van Glabbeek and F. W. Vaandrager. Petri Net Models for Algebraic Theories of Concurrency. In J. W. deBakker, A. J. Nijman, and P. C. Treleaven, editors, PARLE-II , LNCS 259. Springer Verlag, 1987.

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R.J. VAN GLABBEEK & F.W. VAANDRAGER (1987): Petri net models for algebraic theories of concurrency (extended abstract). In J.W. de Bakker, A.J. Nijman & P.C. Treleaven, editors: Proceedings PARLE, Parallel Architectures and Languages Europe, Eindhoven, The Netherlands, June 1987, Vol. II: Parallel Languages, LNCS 259, Springer, pp. 224--242.

No context found.

Rob van Glabbeek and Frits Vaandrager. Petri net models for algebraic theories of concurrency. In Proceedings of PARLE, Volume 259 of the Lecture Notes in Computer Science, pages 224--242, 1987.

No context found.

R.J. van Glabbeek and F. Vaandrager (1987), Petri Net Models for Algebraic Theories of Concurrency, in Proceedings of PARLE 87, J.W. de Bakker et al. (Eds.), Lecture Notes in Computer Science 259, 224--242, Springer-Verlag.

No context found.

R. van Glabbeek and F. Vaandrager. Petri net models for algebraic theories of concurrency. In J. de Bakker, A. Nijman, and P. Treleaven (eds), Proceedings of PARLE '87, Lecture Notes in Computer Science 259, 224--242. Springer-Verlag, 1987.

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R. van Glabbeek and F. Vaandrager. Petri net models for algebraic theories of concurrency. In de Bakker et al. [dBNT87], 224--242. (pp 7, 13)

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R. van Glabbeek and F. Vaandrager, Petri net models for algebraic theories of concurrency, in Proceedings PARLE conference, Eindhoven, Vol. II (Parallel Languages), J. d. Bakker, A. Nijman, and P. Treleaven, eds., vol. 259 of Lecture Notes in Computer Science, Springer-Verlag, 1987, pp. 224--242.

No context found.

R.J. van Glabbeek and F. Vaandrager (1987), Petri Net Models for Algebraic Theories of Concurrency, in Proceedings of PARLE 87, J.W. de Bakker et al. (Eds.), Lecture Notes in Computer Science 259, 224--242, Springer-Verlag.

No context found.

R. J. van Glabbeek & F. W. Vaandrager, Petri Net Model for Algebraic Theories of Concurrency, pp. 224-242, LNCS 259, Spring-Verlag, 1987.

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