P. Huber, A.M. Jenson, L.O. Jepson, and K. Jenson. Towards reachability trees for highlevel petri nets. In G. Rozenberg, ed. Advances on Petri Nets, vol. 188 LNCS, pp. 215-233, Springer-Verlag, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....given in [20] In the past few years there has been a wealth of publications; we attempt to summarise the signi cance of some of these here. 10 State space reduction The basic idea of exploiting symmetries to reduce the size of state spaces is rst investigated within the context of Petri Nets [40, 57]. Ip and Dill [45] apply these ideas to the automatic veri cation of nitestate systems and introduce a new data type, scalarset, to the Mur protocol description language to imply symmetries within a state space. Clarke et al. [16] and Emerson and Sistla [30] discuss symmetry reduction for ....

P. Huber, A.M. Jenson, L.O. Jepson, and K. Jenson. Towards reachability trees for highlevel petri nets. In G. Rozenberg, ed. Advances on Petri Nets, vol. 188 LNCS, pp. 215-233, Springer-Verlag, 1984.

....the planning graphs is polynomial in the size the PrT model. Second, verification through planning graph analysis complies with the concurrent semantics of Petri nets, whereas analysis via reachability trees is essentially based on the interleaving interpretation of concurrence [20] [14]. Let # t t2Fg and t # p2Fg be the precondition predicates and the postcondition predicates of transition t, respectively. Let # p p2Fg and p # t2Fg be the sets of input transitions and output transitions of predicate p, respectively. For a subset of predicates Q P, # Q ....

....respectively. Nevertheless, transition firings in a PrT net may be concurrent. 3. Existing reachability tree based approaches to the reachability analysis of high level Petri nets (PrT nets and Colored Petri nets) such as parameterized reachability tree [20] and symbolic reachability tree [14], suffer from high complexity, which is exponential in the problem size. M is said to be reachable from M 0 if there is such a firing sequence that transforms M 0 to M. Considering the fact that a token in a PrT net may carry structured data and a PrT net is a structure, we will allow a PrT net ....

P. Huber, A.M. Jensen, L.O. Jepsen, and K. Jensen, "Towards Reachability Trees for High-Level Petri Nets," Advances in Petri Nets 1984.

....respectively. Nevertheless, transition firings in a PrT net may be concurrent. Existing reachability tree based approaches to the reachability analysis of high level Petri nets (PrT nets and Colored Petri nets) such as parameterized reachability tree [20] and symbolic reachability tree [14], suffer from high complexity, which is exponential in the problem size. analysis complies with the concurrent semantics of Petri nets, whereas analysis via reachability trees is essentially based on the interleaving interpretation of concurrence [20] 14] Let . t = pP: p,t) F and t . ....

....tree [20] and symbolic reachability tree [14] suffer from high complexity, which is exponential in the problem size. analysis complies with the concurrent semantics of Petri nets, whereas analysis via reachability trees is essentially based on the interleaving interpretation of concurrence [20] [14]. Let . t = pP: p,t) F and t . pP: t, p) F be the precondition predicates and the post condition predicates of transition t, respectively. Let . p = tT: t, p) F and p . tT: p, t) F be the sets of input transitions and output transitions of predicate p, respectively. For a ....

P. Huber, A.M. Jensen, L.O. Jepsen, and K. Jensen, "Towards Reachability Trees for HighLevel Petri Nets," Advances in Petri Nets 1984.

....analysis . of concurrent systems. Unlike the classical methods, we use generic proof metho [10] 11] that avoid the unfolding of a HLPN which leads to a much lesser complexity. For instance, the building of reduced reachability graphs from a HLPN description has been studied in [12] [10] These methods are based on an equivalence relation that exploits the behaviour symmetries in HLPNs. With the help of this relation, a node of the reachability graph is represented by an equivalence class. In [10] this graph is called symbolic reachability graph. Its main advantage is to ....

P. Huber, A.M. Jensen, L.O. Jepsen, K. Jensen, "Towards reachability trees for High-Level Petri Nets", Advances in Petri Nets'84, pp 215-233, 1984.

....investigate other classes of nets for which we believe that symbolic markings can be defined. However some classes of colored nets with particular symmetry types cannot be analyzed this way. Therefore, we will try to extend to the stochastic analysis of a model the reachability tree defined in [Hub 84] for colored nets. ....

P. Huber, A.M. Jensen, L.O. Jepsen, and K. Jensen, "Towards Reachability Trees for High Level Petri Nets", 5th European Workshop on Application and Theory of Petri Nets, Aarhus, Denmark (1984).

....SRG, which can be much less than the number of ordinary markings generated by the Place Transition net (P T) resulting from the unfolding of the RN. Some kinds of symbolic marking representations to exploit the symmetries of the reachability graph (RG) have already been proposed for general CPNs [12, 13, 7, 14] as well, but in all these cases heuristics were needed to decide the type of aggregations. These heuristics were based on an explicit knowledge by the modeler of the symmetries present in a particular model. Thus none of these methods could be implemented in a general algorithmic form. From this ....

P. Huber, A.M. Jensen, L.O. Jepsen, and K. Jensen. Towards reachability trees for high-level Petri nets. In G. Rozenberg, editor, Advances on Petri Nets '84, volume 188 of LNCS, pages 215-233. Springer Verlag, 1984.

....In the case of complex target systems, solving the reachability problem either requires radical model simplifications or extremely long run times. In the literature, a number of methods are proposed for efficient reachability analysis, each having its advantages and drawbacks. The symmetry method [4] needs the help of the analyst. Stubborn sets [7] and incomplete reachability analysis [3] in its original form aim at only finding deadlocks. Symbolic model checking [6] uses binary decision diagrams (BDD) to analyze huge state spaces, however, it is not guaranteed that most distributed systems ....

P. Huber, A. M. Jensen, I. O. Jensen, and K. Jensen. Towards reachability trees for high-level Petri-nets. Technical report PD-174, DAIMI, Dept. of Computer Science, Aarhus University, 1985.

.... is inherent to the representation of the parallelism by interleaving, and it is addressed by methods such as the stubborn sets method based upon the notion of dependence between transitions [16] the covering markings method which takes into account situations where some places become unbounded [4, 9], or the Covering Step Graph method which avoids intermediate markings [18] Secondly, the reachability graph of a high level Petri net may be of a large size because each transition occurrence is characterized by the transition which is occurring and in addition by the tokens involved in this ....

....and in addition by the tokens involved in this occurrence. To cope with this problem, the idea is to develop techniques to build reduced reachability graphs while disregarding the value of tokens involved in transition occurrences. The original idea of reduced reachability graph was proposed in [9] for coloured Petri nets: the intrinsic symmetries of the model, which result in many different portions of the graph representing the same behaviour, are detected. Similar methods for the reduction of reachability graphs have been introduced for others models such as parametrized reachability ....

: P. Huber, AM. Jensen, LO. Jepson, K. Jensen. "Towards reachability Trees for High-Level Petri Nets", 5th European Workshop on Applications and Theory of Petri Nets. Aarhus, Denmark, 1984.

....that must be explored by temporal logic model checking algorithms. Unfortunately, there has been relatively little research in the past on exploiting symmetry for this purpose. Most of the work on this problem has been performed by researchers investigating the reachability problem for Petri nets [64]. However, their work does not consider general temporal properties nor the complications that are caused by representing the state space using OBDDs. Recently, the use of symmetry in model checking has been investigated by several authors [32, 40] We briefly outline the results on the use of ....

P.Huber, A. Jensen, L. Jepsen, and K. Jensen. Towards reachability trees for high-level petri nets. In G. Rozenberg, editor, Advances on Petri Nets, 1984.

....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 ....

P. Huber, A.M. Jensen, L.O. Jepsen, and K. Jensen. Towards reachability trees for high--level Petri nets. In Advances in Petri Nets 1984, LNCS 188, pages 215--233, 1984.

....sufficient for an efficient implementation of the for all symmetries loop and the partition of net elements into equivalence classes. These two constructions are the usual way to integrate symmetries into an analysis algorithm. 1 Introduction Symmetries of Petri nets have been introduced in [HJJJ84] for reducing the size of the reachability graph for coloured Petri nets. In [Sta91] the idea of symmetric reduction was applied to the reachability graph of place transition nets. Meanwhile the state space of Petri nets with time restrictions can be reduced as well ( RS97] The application of ....

....require knowledge about the net symmetries. There are three major approaches to provide this knowledge: 1. The user comes up with a description of net symmetries; 2. Symmetries are deduced from the syntax of high level net inscriptions; 3. A tool calculates the symmetries. The first approach ([HJJJ84, Jen96]) is based on the assumption that the one who generates the net model is familiar with the modelled system and knows the symmetries. This assumption might be realistic when a net model is drawn directly. However, when a net model is generated by the translation of another description language, or ....

[Article contains additional citation context not shown here]

P. Huber, A.M. Jensen, L.O. Jepsen, and K. Jensen. Towards reachability trees for high--level Petri nets. In Advances in Petri Nets 1984, LNCS 188, 215--233, 1984.

....compensated by the ability to exclude whole blocks of symmetries from the iteration. 1 High level versus low level symmetries Symmetries turned out to be a suitable tool for decreasing the size of state graphs and reduced state graphs of Petri nets. This was first observed for high level nets [HJJJ84]. In [Sta91] the approach was transferred to low level Petri nets. In the area of high level nets, we think about symmetries as permutations of the colour domains. The present approaches are restricted to symmetry groups that are composed from a small set of standard permutation groups of the ....

....nets, we think about symmetries as permutations of the colour domains. The present approaches are restricted to symmetry groups that are composed from a small set of standard permutation groups of the colour domains, namely rotation groups, the group of all permutations, and the trivial group. In [HJJJ84], the user is required to come up with a description of a feasible symmetry group. For this purpose, we assume the tool user to be familiar with the modeled system. In [CDFH90] symmetries are deduced automatically from the net inscriptions. This approach seems to rely on the use of a rather ....

P. Huber, A.M. Jensen, L.O. Jepsen, and K. Jensen. Towards reachability trees for high--level Petri nets. In Advances in Petri Nets 1984, Lecture Notes on Computer Science 188, pages 215--233, 1984.

....[25, 26] and for the derivation of operational bounds [27] 2.2. 1 The Symbolic Reachability Graph Structural symmetries in HLPN models, often lead to behavioral symmetries that can be exploited to reduce the computational cost of analysis methods based on the reachability graph construction [28, 25]. The Regular Net (RN) and Well Formed Colored Petri Net (WN) formalisms [25, 29] have been introduced to systematize the symmetry exploitation technique: behavioral symmetries of models described with this formalisms can be automatically discovered and exploited. This goal is achieved by ....

P. Huber, A.M. Jensen, L.O. Jepsen, and K. Jensen. Towards reachability trees for high-level Petri nets. In G. Rozenberg, editor, Advances on Petri Nets '84, volume 188 of LNCS, pages 215--233. Springer Verlag, 1984.

....It is possible to reduce verification effort by taking into account symmetries and letting an equivalence class of states be represented by one state. Valmari has shown [78] that the stubborn set method is compatible with the symmetry method presented by Huber, Jensen, Jepsen, and Jensen [37] as far as the detection of reachable terminal states is concerned. Later, Tiusanen has shown [69] that the stubborn set method is compatible in a very wide sense with the more general symmetry method presented by Starke [68] and Schmidt and Starke [67] The symmetry method in [37] includes an ....

....and Jensen [37] as far as the detection of reachable terminal states is concerned. Later, Tiusanen has shown [69] that the stubborn set method is compatible in a very wide sense with the more general symmetry method presented by Starke [68] and Schmidt and Starke [67] The symmetry method in [37] includes an algorithm that checks whether two states are equivalent or not. Starke and Schmidt have not presented any corresponding algorithm, but, as mentioned by Clarke, Filkorn, and Jha [12] a unique representative of the equivalence class of a state can be computed using Bryant s BDD s ....

Huber, P., Jensen, A.M., Jepsen, L.O., and Jensen, K.: Towards Reachability Trees for High-Level Petri Nets. Aarhus University, Department of Computer Science, Technical report DAIMI PB-174, Aarhus 1985, 19+42 p.

....as State Space Explosion. Among the techniques being developed for countering this problem are partial order methods, abstraction, compositional approaches, and symmetry reductions. Symmetries abound in hardware circuits, distributed algorithms and concurrent programs. Huber, Jepsen and Jensen [HJJ84] and Starke [Sta91] have investigated the use of symmetries for expediting reachability analysis for Petri nets. An algebraic approach for reducing the cost of protocol analysis has been proposed by Kurshan [Kur87] and Attie and Emerson [AE89] The approach uses quotient structures induced by ....

P. Huber, L. Jepsen, and K. Jensen. Towards Reachability Trees for High-level Petri Nets. In G. Rozenberg, editor, Advances on Petri Nets, pages 215--233, 1984.

....varies considerably. Some present exact formal denitions and complete proofs (Chapters 2 and 4) while others seek to give a good intuition by semiformal descriptions and examples. This inconsequence is motivated below. The symmetry method is originally presented in a seemingly formal way [11]. The exactness does not, however, extend down to the roots of the denitions. Since the low level is not obvious and it is naturally needed in the application of the method, it is dened in detail in Chapter 2. The denitions have also been formulated slightly dioeerently and they have been ....

....kinds of symmetrical structures that seem to lead to a severe redundancy in the construction of the reachability graph. A research group consisting of Peter Huber, Arne M. Jensen, Leif O. Jepsen and Kurt Jensen has presented a method that formalises some types of symmetries in Petri systems [11] so that symmetrical markings are represented by a single vertex and symmetrical transitions by a single edge in the compressed reachability graph. Figure 2 represents a coloured system model of the dining philosophers. When constructing the reachability graph, one immediately meets with a ....

[Article contains additional citation context not shown here]

Huber, P., Jensen, A.M., Jepsen, L.O. and Jensen, K.: Towards Reachability Trees for High-level Petri Nets. Technical report DAIMI PB174, Department of Computer Science, Aarhus University, Aarhus 1985, 19+42 p.

....A is in the critical section and B is waiting is, for all practical purposes, equivalent to the state in which B is in the critical section and A is waiting. The basic idea of exploiting symmetries to reduce the state space in automatic verification is not new. It was described by Huber et al. [HJJJ84] for high level Petri nets. The idea was further developed by Starke [Sta91] for deadlock and liveness checking in P T nets. In unpublished work, Clarke, McMillan and Jha at Carnegie Mellon, and (independently) Emerson and Kaufman at the University of Texas have applied the idea to CTL ....

Peter Huber, Ame M. Jensen, Leif O. Jepsen, and Kurt Jensen. Towards Reachability Trees for High-level Petri Nets. In G. Rozenberg, editor, Advances on Petri Nets '84, Springer Verlag, pp. 215--233, 1984.

....the time and other resources needed to inspect all states in the space. Fortunately, many properties can often be veri ed without inspecting all reachable states of the system. In this report, we consider two promising methods for alleviating the state space explosion problem: the symmetry method [1, 4, 5] and the stubborn set method [6, 7, 8] We concentrate on the computation of symmetries and stubborn sets. We use place transition nets [3] as our formalism. This is a tolerable restriction since many models of concurrency can be transformed into behaviourally equivalent place transition nets. ....

....(M [oei f for short) ioe for each n 2 N; the pre x of length n of oe is f enabled at M: 2 An in nite transition sequence is merely a function. It can be thought of as occurring as a path in the full reachability graph ioe it is enabled at some reachable marking. 3 Symmetries The symmetry method [1, 4, 5] produces a virtual reachability graph containing for each reachable marking one and only one member of the equivalence class of the marking, the corresponding equivalence relation being determined by the symmetries of the net. De nition 3.1 Let hS; T ; F; K;W;M 0 i be a place transition net. ....

Huber, P., Jensen, A.M., Jepsen, L.O., and Jensen, K.: Towards Reachability Trees for High-Level Petri Nets. Aarhus University, Department of Computer Science, Technical report DAIMI PB-174, Aarhus 1985, 19+42 p.

....the system state. Although the modelling technique based on SPNs is much easier to use than classical Markovian modelling techniques, it still can lead to models whose size is too large when dealing with realistic systems. Several researchers have faced this problem and proposed new classes of SPN [12, 13, 14, 15] which can be used for the construction of more compact models. One of these classes, Stochastic Well Formed Nets, is described in this section. We assume that the reader is familiar with basic concepts from untimed Petri nets and SPNs details about the formalisms may be found for example in ....

P. Huber, A.M. Jensen, L.O. Jepsen, and K. Jensen. Towards reachability trees for high-level Petri nets. In G. Rozenberg, editor, Advances on Petri Nets '84, volume 188 of LNCS, pages 215--233. Springer Verlag, 1984.

No context found.

Peter Huber, Ame M. Jensen, Leif O. Jepsen, and Kurt Jensen. Towards Reachability Trees for High-level Petri Nets. Advances on Petri Nets, 1984.

No context found.

Peter Huber, Ame M. Jensen, Leif O. Jepsen, and Kurt Jensen. Towards Reachability Trees for Highlevel Petri Nets. Advances on Petri Nets, 1984.

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