Wolfgang Reisig. Petri nets and algebraic specifications. Theoretical Computer Science, 80:1--34, March 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a formal specification technique for distributed and concurrent systems. High level nets can be considered as the integration of process and data type description, most prominent classes are Coloured Petri nets [Jen92, Jen95] Predicate Transition nets [GL81, Gen91] and algebraic high level nets [Vau87, Rei91, PER95]. The practical relevance of high level Petri nets is considered to be very high, as there are many high level Petri net tools used in real software production (e.g. LEU [SM97] Design CPN [JCHH91] INCOME [OSS94] Since algebraic specifications are well developed for abstract data types (see ....

W. Reisig. Petri Nets and Algebraic Specifications. Theoretical Computer Science, 80:1--34, 1991.

....model of this kind with a more set theoretic avour. They generalize PTNs in such a way that tokens can be arbitrary set theoretic objects. Quite di erent from, but closely related to, colored nets are high level Petri nets that use an algebraic speci cation language as an underlying formalism [76, 6, 77, 67, 65, 66, 22, 5]. 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 ....

....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 how an executable ....

W. Reisig. Petri nets and algebraic specications. Theoretical Computer Science, 80:1-34, 1991.

....nets. Typical examples are the following combinations: indexed sets with place transition nets leading to Coloured Petri nets, predicate logic with elementary nets leading to predicate transition nets [9] algebraic speci cations with place transition nets leading to algebraic high level nets [25,28], ML with place transition nets leading to Coloured Petri nets [11] OBJ2 with superposed automata nets leading to OBJSA nets [1] and algebraic speci cations with the Petri Box Calculus [2] leading to M nets [17] Object oriented analysis and programming techniques are currently the de facto ....

W. Reisig. Petri Nets and Algebraic Specications. Theoretical Computer Science, 80:134, 1991.

....If you are unsure about their theoretical foundations, do not use them. No compromises where made in the simulation engine to allow their implementation, so that robustness of Renew is not a ected. 3.9. 1 Flexible Arcs Flexible input arcs and exible output arcs were introduced by Reisig in [12]. They allow multiple tokens to be moved by a single arc. Moreover, the token values and even the number of tokens may vary with the binding of the transition s variables. Renew 1.2 In Renew, these arcs are indicated by attaching two arrowheads instead of one to the end of the arc. In the ....

Wolfgang Reisig. Petri nets and algebraic specications. Theoretical Computer Science, 80(1-2):1-34, 1991.

....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 ....

W. Reisig. Petri nets and algebraic specications. Theoretical Computer Science, 80:134, March 1991.

....transformations, which ensures consistency among models in di erent development steps. Moreover, we de ne and investigate net class transformations between elementary nets [RE98] place transition nets, marked nets (see e.g. DR98] and a new variant of algebraic high level nets, similar to [Vau87, Rei91, PER95]. In contrast to the classical notion, see e.g. PER95] the new de nition comprises explicit variables and a new de nition of morphisms. The laxer notion of morphisms allows substituting variables with terms and thus a wider applicability of rules. The paper is structured as follows: In Section ....

W. Reisig. Petri Nets and Algebraic Specications. Theoretical Computer Science, 80:1-34, 1991.

....logic and high level nets with special emphasis on ECATNets. The main motivation of this correspondence is the need to have an ECATNet model which is more expressive and can capture complex properties including positive and negative ones. A relationship between algebraic high level nets of Reisig [16] and intuitionistic predicate linear logic has been already pointed out in [13] Lilius establishes in [13] a correspondence between the two models in several steps. First he shows how a Petri net gives rise to a model of linear logic [7] and proves that the construction is functorial. Then he ....

....pointed out in [13] Lilius establishes in [13] a correspondence between the two models in several steps. First he shows how a Petri net gives rise to a model of linear logic [7] and proves that the construction is functorial. Then he shows how an algebraic high level net gives rise to a Petri net [16]. This construction is also proved to be functorial. Finally, the result desired is the composition of two functors. A similar approach can be directly used since an ECATNet is naturally transformed in a simple Petri net model [3] However, regarding the natural definition of an ECATNet in ....

W. Reisig, Petri Nets and Algebraic Specifications, Theoretical Computer Science, 80(1991), pp. 41-64.

....not lead to a complicated implementation of the simulation algorithm. The implemented inhibitor arc formalism is less general than that presented in [2] but it su ces for many applications. The clear arcs behaviour matches that described in [2] Flexible arcs are related to those presented in [3], but syntactic variations were necessary to make them usable together with Java inscriptions, since Java does not naturally support multisets. Renew allows the users to save an entire system of nets for later stand alone simulation. This way the Petri nets become independent of the graphical ....

Wolfgang Reisig. Petri nets and algebraic specications. Theoretical Computer Science, 80(12):134, 1991.

....and conceptual levels. The techniques possess a clear and intuitive graphical representation which often makes it possible for a system to be visualized by looking at its corresponding net model. The mathematical foundations of Petri net theory provide sound methods for the analysis of Petri net [72, 86, 94] and coloured Petri net [59, 100, 26, 25, 27, 46, 62, 63, 64] models. In general, a Petri net comprises a bipartite directed graph consisting of a set of places, a set of transitions, a set of arcs (connecting transitions to places and places to transitions) together with the associated ....

W. Reisig. Petri nets and algebraic specifications. Theoretical Computer Science, 80, 1991.

....which combines fault tolerance, replication, and logging. 3 2 The protocol In this section, we present the protocol for the fault tolerant execution of a parallel program. Moreover, we characterize the faults that are tolerated by the protocol. As a formal model, we use algebraic Petri nets [30] equipped with di#erent arc types [23] For the time being, we can ignore these special features we will come back to the di#erent arc types in Sect. 4.1.3. 2.1 The setting Before introducing the model, we discuss our view of a parallel program. We assume that a parallel program consists of a ....

Wolfgang Reisig. Petri nets and algebraic specifications. Theoretical Computer Science, 80:1--34, May 1991.

....ed in DAWN we refer to [9, 8, 14, 13] In DAWN, we proceed in three steps: modelling, speci cation, and veri cation. These steps will be explained below. 1 ILF stands for Integrating Logical Functions. 1 2. 1 Modelling In DAWN, a distributed algorithm is modelled by an algebraic Petri net [12, 7]. The Petri net shown in Fig. 1 models the following algorithm: For a given set of agents A, each agent cyclically adopts the state p, q , and r ; the agents do not interact at all. Initially, each agent is in state p. In a Petri net, possible states are given by a set of places, which are ....

Wolfgang Reisig. Petri nets and algebraic specications. Theoretical Computer Science, 80:1-34, May 1991.

....5.1 Prerequisites We start with an informal introduction of some basic algebraic notions. A formal definition of these notions can be found in [KR96] Readers familiar with algebraic specifications and algebraic Petri nets may skim this section; the notions and notations are taken from [KR96,Rei91] Multisets In contrast to sets in multisets multiple occurrences of elements are possible. For a set A we denote the set of all multisets over A by N A . For an element a we denote the number of occurrences of a in a multiset m by m[a] Signatures and algebras A signature represents the ....

Wolfgang Reisig. Petri nets and algebraic specifications. Theoretical Computer Science, 80:1--34, 1991.

....1 . The tokens added or removed by the occurrence of a transition are represented by arc inscriptions. However, the same transition may occur in several modes. Therefore, the inscription is a functional object which associates a collection of tokens to each mode. Algebraic Nets: Algebraic Nets [Kra85, Bil89, Rei91] are a special version of Coloured Petri Nets, where the allowed token domain is specified by algebraic techniques. From the semantical point of view, there seems to be no difference at first glance. For technical reasons, most versions of) Algebraic Nets have one special semantical feature, ....

Wolfgang Reisig. Petri nets and algebraic specifications. Theoretical Computer Science, 80:1--34, May 1991.

....Petri net in this concurrent run. 3 High level Petri nets and concurrent runs This section is the basis for the formal treatment. We de ne syntax and semantics of high level Petri nets. The reader familiar with DAWN may skip this section. The notions and notations are taken from [KR96,WWV 97,Rei91] 3.1 Preliminaries An algebra A = A; Op) consists of a universe A and set Op of operations on A. Each operation f 2 Op has a functionality f : A 1 A 2 : A n A n 1 such that each A i A. For each set A, we denote by 2 A the powerset, i.e. the set of all subsets of A. A sorted set ....

.... is a reachable state of if there is a concurrent run which contains a cut C which satis es r(C) M . 4 Properties of distributed algorithms To reason about properties of an algorithm, we need a formalism to express the properties. In DAWN, a linear time temporal logic is used [WWV 97,Rei91] We de ne state properties which are interpreted over markings and temporal properties which are interpreted over concurrent runs. The basis of state properties for a given high level Petri net are terms of sort bool of the algebra A. We also use the names of the places of as variables in the ....

W. Reisig. Petri Nets and Algebraic Specications. Theoretical Computer Science, 80:1-34, May 1991.

....logic and high level nets with special emphasis on ECATNets. The main motivation of this correspondence is the need to have an ECATNet model which is more expressive and can capture complex properties including positive and negative ones. A relationship between algebraic high level nets of Reisig [16] and intuitionistic predicate linear logic has been already pointed out in [13] Lilius establishes in [13] a correspondence between the two models in several steps. First he shows how a Petri net gives rise to a model of linear logic [7] and proves that the construction is functorial. Then he ....

....pointed out in [13] Lilius establishes in [13] a correspondence between the two models in several steps. First he shows how a Petri net gives rise to a model of linear logic [7] and proves that the construction is functorial. Then he shows how an algebraic high level net gives rise to a Petri net [16]. This construction is also proved to be functorial. Finally, the result desired is the composition of two functors. A similar approach can be directly used since an ECATNet is naturally transformed in a simple Petri net model [3] However, regarding the natural de nition of an ECATNet in ....

W. Reisig, Petri Nets and Algebraic Specications, Theoretical Computer Science, 80(1991), pp. 41-64.

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Wolfgang Reisig. Petri nets and algebraic specifications. Theoretical Computer Science, 80:1--34, March 1991.

....to verication and calculation of symbolic siphons traps. However, due to the duality of siphons and traps, we restrict ourselves to siphons. The corresponding results for traps can be easily obtained by changing the direction of the arcs. For basic denitions concerning algebraic nets, we refer to [Rei91, Sch96d, Sch95]. Supported by a scholarship of German Academic Exchange Service (DAAD) 2 Commoner s Theorem for algebraic nets with innite color domains While the relation between siphons, traps and dead markings still holds for nets with innite color domains, there is a highlevel free choice net which is ....

W. Reisig. Petri nets and algebraic specications. Theoretical Computer Science, 80:134, 1991.

....technique for distributed and concurrent systems. High level nets can be considered as the integration of process and data type description. Some of the most prominent classes are Coloured Petri Nets [Jen92,Jen94,Jen97] Predicate Transition nets [GL81,Gen91] and algebraic high level nets [Vau87,Rei91,PER95]. Coloured Petri Nets are the focus of this paper, since they are widely known and constitute a very popular class of highlevel Petri nets. The practical relevance of Coloured Petri Nets is considered to be very high, not at least due to the successful tool Design CPN [JCHH91] In the area of ....

W. Reisig. Petri Nets and Algebraic Specifications. Theoretical Computer Science, 80:1--34, 1991.

....initial marking greater than 0 and every transition can only be connected to finitely many places via a direct arc (with multiplicity greater than 0) On the other hand, places can be connected to infinitely many transitions. For further details according to algebraic Petri nets, please refer to [Rei91]. Definition 5 (Siphon,Trap) A subset D of P is a siphon a net N = P; T ; F ] iff FD DF . D is a trap iff DF FD. For an algebraic net, siphons and traps are those of the underlying place transition net. 3 Term based set al..gebra One of the major reasons which make our approach work for ....

W. Reisig. Petri nets and algebraic specifications. Theoretical Computer Science, 80:1--34, 1991.

....algorithms exist to determine the functional properties of nets. They are a promising tool for describing and studying information processing systems that are characterised as being concurrent, asynchronous, distributed, parallel, nondeterministic and or stochastic. 1 High level algebraic nets [35, 30, 4] have been introduced in order to exploit the rich theory of algebraic speci cations for high level Petri nets: Petri nets gain a great deal of modelling power by representing dynamically changing items as structured tokens whereas algebraic speci cations turned out to be an adequate and exible ....

W. Reisig. Petri Nets and Algebraic Specications. Theoretical Computer Science, 80:1-34, 1991.

....of HAN for reactive distributed systems development are listed and the link between the HAN model to the SANDS development environment is summarised. 1. INTRODUCTION The interest of the mixed use of algebraic specifications and Petri nets (introducing a new basic class called algebraic nets [1]) has been shown in many papers since 1985. Several models have been defined and are now focused on the structuring primitives used. The principle of hierarchical construction of the specification has already been used in some Petri net models, for example hierarchical coloured nets [9] but, ....

....be found in [3] and references including hierarchical algebraic specifications are given in [4] 3.2 Algebraic Nets We have chosen to define the algebraic net modules, which are the basic component of hierarchical algebraic nets, as a mixing of the approaches of J. vautherin [5] and W. Reisig [1]. In algebraic nets a key point concerns the places definition. A place is a multiset of typed values : 1) J. Vautherin considers the multisets at a semantic level by enhancing the AS models to multisets; 2) W.Reisig considers the multisets at the syntactic level by adding an algebraic ....

W.Reisig, 'Petri nets and Algebraic specifications', Theoretical Computer Science, n80, pp 1-34, 1991.

....models a process run that recovers the original system state. Thus, Tinvariants are an important means for proving correctness of the system. The significance and easy calculation in low level nets is the motivation in this paper for transferring the notion of T invariants also to AHL nets [PER95, Vau87, Rei91]. AHL nets consist of Petri nets for the process description and algebraic specifications [EM85] for the data type description. In general, the integration of data and process information into one formal specification technique leads to high level nets (see e.g. Jen81, Jen92, GL81, Gen91] In ....

....the variable assignments for the variables of each transition. 3 3 Review of AHL Nets We now introduce basic definitions of AHL nets, their behaviour and modification via morphisms as given in [PER95] Further information about different kinds of algebraic Petri nets can be found for instance in [Vau86, KS91, Rei91, EPR94b, Lil94]. In contrast to other variants of algebraic highlevel nets ( DHP91, Hum89, Lil94] we do not label places with sorts. Note, that the pre and post domain of a transition is given by a multiset of pairs of terms and places, i.e. as elements of a commutative monoid. Here, we use free commutative ....

W. Reisig. Petri Nets and Algebraic Specifications. Theoretical Computer Science, 80:1--34, 1991.

....to ( t; p] d) c) By the translation of algebraic Petri nets to colored nets and further into place transition nets all behavioral aspects can be traced back to the definitions which are well known for place transition nets. For further details according to algebraic Petri nets, please refer to [Rei91, Sch96c]. 3 Getting started In the remaining part of the paper we study the particular reduction rules one per section. All these sections are organized in the same way. First, we repeat the low level rule. We stick to the notations in [Sta90] We present the application condition and the ....

W. Reisig. Petri nets and algebraic specifications. Theoretical Computer Science, 80:1--34, 1991.

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W. Reisig. Petri Nets and Algebraic Specifications. Theoretical Computer Science, 80:1--34, 1991.

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W. Reisig. Petri Nets and Algebraic Specications. Theoretical Computer Science, 80:1-34, 1991.

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