Ekkart Kindler and Hagen V olzer. Flexibility in algebraic nets. In J org Desel and Manuel Silva, editors, Application and Theory of Petri Nets 1998: 19th International Conference, ICATPN'98, volume 1420 of Lecture Notes in Computer Science, pages 345--364, Lisbon, Portugal, June 1998. Springer-Verlag, Berlin, Germany.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....language facilitates straightforward translation of data types and constructs found in SDL and high level programming languages. Despite its expressive power, the Maria modelling language has a sound theoretical foundation. The semantics has been defined in [17] in terms of Algebraic System Nets [10]. The first usable versions of the analyser were released in the summer of 1999. Since then, Maria has been in extensive internal use, which has helped in finding and correcting errors and performance bottlenecks. In 2001, a graphical user interface for exploring state spaces and displaying query ....

Ekkart Kindler and Hagen V olzer. Flexibility in algebraic nets. In J org Desel and Manuel Silva, editors, Application and Theory of Petri Nets 1998: 19 International Conference, ICATPN'98, volume 1420 of Lecture Notes in Computer Science, pages 345--364, Lisbon, Portugal, June 1998. Springer-Verlag.

....Due to the fact that MEL generalizes MSA in an obvious way, ANSs over MEL are a straightforward generalization of ANSs over MSA, i.e. many sorted algebraic net speci cations. Disregarding the issue of the underlying speci cation language, the de nition we give below is equivalent to the one in [41, 43], generalizing [65] by so called exible arcs, which transport variable multisets of tokens in the sense that the number of tokens transported by an arc is not xed but can depend on the mode in which the associated transition occurs. Later, in Section 4.3 we will illustrate by means of an example ....

E. Kindler and H. Volzer. Flexibility in algebraic nets. In J. Desel and M. Silva, editors, Application and Theory of Petri Nets

....similar to the procedure presented in this work, as it also is a Tarjan based on the AEy algorithm. 4 Implementation The model checking procedure described in this work has been implemented in the MARIA analyzer [21] The MARIA analyzer is a reachability analyzer for algebraic system nets [15, 16, 25] and it has been developed at the Laboratory for Theoretical Computer Science at Helsinki University of Technology. 4.1 The MARIA analyzer The MARIA analyzer, is a reachability analyzer for Algebraic System Nets. The intention is to develop an analyzer with model checking capabilities for a ....

E. Kindler and H. V#lzer. Flexibility in algebraic nets. In Proceedings of the International Coneference on Application and Theory of Petri Nets

....based calculi for high level Petri nets will cover properties of the full multi region calculus, such as the possibility of cut elimination, and possibilities of using conditional rewriting logic ( Mes92] for LLPNs with underlying multi region calculi. The approach of using flexible arcs as in [KV98] seems also to be worthwhile studying for Linear Logic semantics for dynamic Petri net structures. Using flexible multisets as arc inscriptions could prove to be a solution to the problem of removing all formulae that belong to the encoding of the same transition. ....

E. Kindler and H. Volzer. Flexibility in Algebraic Nets. In Desel and Silva [DS98].

....Tommi A. Junttila Finding Symmetries of Algebraic System Nets 3. Algebraic System Nets In this section we introduce a high level Petri net formalism called algebraic system nets. Basically, an algebraic system net is a Petri net augmented with algebraic de nitions. The presentation is based on [22, 23, 26]. Some basic notations must be de ned rst. In the rest of the paper, we use the set B = ftrue; falseg for Boolean values and N = f0; 1; 2; g for natural numbers. For two sets, A and B, A B] means the set of all functions from A to B. For a set A, MS(A) denotes the set of all multi sets ....

....which are special cases of signatures and algebras, respectively. We distinguish some ground sorts and assign each of them a corresponding multi set sort. The domain of a multi set sort is the set of all multi sets over the domain of the corresponding ground sort. The de nition is based on [22, 23]. However, we use a stricter de nition in the sense that we require that each sort is either a ground sort or a multi set sort. This is a mere technicality because we can always augment the set of sorts by the corresponding (multi set) sorts even though we actually never use them. For a signature ....

E. Kindler and H. Volzer. Flexibility in algebraic nets. In J. Desel and M. Silva, editors, Application and Theory of Petri Nets 1998; Proceedings of the 19th International Conference, ICATPN'98; Lisbon, Portugal, June 1998, volume 1420 of Lecture Notes in Computer Science, pages 345-364. Springer-Verlag, Berlin, Germany, 1998.

....this section, we formalize arc typed Petri nets and their runs. Basically, this semantical model corresponds to basic high level nets [11] it is the underlying semantical model of arc typed Petri nets as de ned in [10] For a syntactical representation and a more detailed motivation, we refer to [10, 9]. Multisets We start with some basic notation. For some set D, a mapping m : D N such that P d2D m(d) 2 N is called a bag over D. The set of all bags over some set D is denoted by B(D) Petri nets We call N = P; T; F ) a Petri net if P and T are two disjoint sets and F (P T ) T P ....

....a family (F c ) c2C such that the above constraints are met. We x this arc typed net for the rest of this paper. Occurrence nets Next, we formalize runs of the arc typed Petri net. Basically, a run of the arc typed Petri net is a process [3] of the Petri net as de ned for algebraic Petri nets [10, 9]; the di erent arc types of the arc typed net carry over to the run canonically. A run is a labelled occurrence net, where an occurrence net K = B; E; is Petri net such that the transitive closure of is acyclic, such that each element of K has only nitely many predecessors with respect ....

Ekkart Kindler and Hagen Volzer. Flexibility in algebraic nets. In J. Desel and M. Silva, editors, Application and Theory of Petri Nets

....understandable way. Often, many details which are necessary for formal correctness obscure the basic idea of the proof. As a result, proofs are either formalistic rather than formal or proofs are sloppy rather than intuitively understandable. The Distributed Algorithms Working Notation (DAWN) [24, 21, 14, 22] was developed to model and verify distributed algorithms in an intuitive way. Proofs are on a high level of abstraction which helps to focus on the basic idea rather than on formalistic details (e.g. 13, 22, 8] Due to the high level of abstraction, some details might be easily ....

....in detail, we brie y introduce DAWN by an example. The example shows how to model and verify distributed algorithms in DAWN. We consider a simple protocol of negotiating agents (cf. 24, 21] 1. 1 Modelling In DAWN, distributed algorithms are modelled by a particular kind of algebraic Petri nets [12, 14]. The model of the negotiation protocol is shown in Fig. 1. We assume that there is a set of agents U participating in the negotiations. Moreover, we assume that agents do not meet personally, but communicate by sending and receiving messages. Each agent x 2 U may adopt two states: Either, it ....

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E. Kindler and H. Volzer. Flexibility in algebraic nets. In J. Desel and M. Silva (eds.), Application and Theory of Petri Nets 1998, 19 th International Conference, LNCS 1420, pp. 345-364. Springer-Verlag, June 1998.

....systems. 3.1. 1 The DAWN approach DAWN supports the modelling and the veri cation of distributed algorithms [WWV 97, Rei98] The algorithms are modelled by the help of a special version of algebraic Petri nets and are veri ed by a combination of Petri net techniques and temporal logic [KR97, KV98b] A distributed algorithm runs on a network of independent computing units called agents. The agents can only communicate via asynchronous messages which are sent along prede ned communication channels of the network. Typically, a distributed algorithm is not designed for a particular network ....

E. Kindler and H. Vlzer. Flexibility in algebraic nets. In J. Desel and M. Silva, editors, Application and Theory of Petri Nets 1998, 19 th International Conference, volume 1420 of LNCS, pages 345364. Springer-Verlag, June 1998.

....[23] Here, we formalize a more general version of flexible arc, the idea of which can already been found in [7] We call the resulting class algebraic system nets. The P invariant calculus of Reisig [23] can be adapted to algebraic system nets, which will be demonstrated in a forthcoming paper [16]. We add two more features to algebraic system nets, which have been shown to be necessary for adequately modelling distributed systems [24] the distinction of progress and external transitions and fair arcs [18] When talking about a distributed algorithm we actually do not talk about a single ....

Ekkart Kindler, Wolfgang Reisig, and Hagen Volzer. Flexibility in algebraic nets. In preparation, 1996.

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Ekkart Kindler and Hagen V olzer. Flexibility in algebraic nets. In J org Desel and Manuel Silva, editors, Application and Theory of Petri Nets 1998: 19th International Conference, ICATPN'98, volume 1420 of Lecture Notes in Computer Science, pages 345--364, Lisbon, Portugal, June 1998. Springer-Verlag, Berlin, Germany.

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