Wolfgang Reisig. Petri nets and algebraic specifications. Theor. Comput. Sci., 80(1):1--34, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....been presented. For example, combinations of an algebraic specification language with ffl a process calculi: other than LOTOS, we have PSF, 11, 12] a combination of a process calculs similar to ACP with ASF (Algebraic Specification Formalism) 3] ffl Petri nets [15] many proposals see, e.g. [16, 2, 5, 21] ffl statecharts [7] see in [14] a combination prepared following the method proposed here. But, there are also combinations using Z for the data part, for example with statecharts [4, 22] and with an object oriented language as Object Z [17] On the other hand, fixing some (even powerful) ....

W. Reisig. Petri Nets and Algebraic Specifications. T.C.S., 80:1--34, 1991.

....to the CO OPN 2 language. Keywords: CO OPN, Petri nets, real time, linear temporal logic. 1 Introduction Motivation CO OPN 2 [2] is an object oriented specifications formalism based on algebraic data types [7] ADT) and Petri nets which are combined in a way that is similar to algebraic nets [6]. Algebraic specifications are used to describe the data structures and the functional aspects of a system, while Petri nets allow to model the system s concurrent features. To compensate for algebraic Petri nets lack of structuring capabilities, CO OPN 2 provides a structuring mechanism based on ....

....t # [2, 10] Similarly, from any other reachable marking, method move and put can fire at any time in the interval [5, 10] respectively [2, 10] after transition processing has emptied place p2. For instance, if processing occurs at time 6, then method put can occur at any time in the interval [6, 10]. 3.3 Examples Figure 6 shows three cases related to condition Cond (weak time semantics wrt strong time semantics) The initial marking is such that places p1 and p2 have one token each, stamped with time 0: Case a: m1 must fire at 5. In the weak time semantics it may occur that method m1 ....

W. Reisig. Petri nets and algebraic specifications. In Theoretical Computer Science, volume 80, pages 1--34. Elsevier, 1991.

....synchronization graph is smaller than the size of the ordinary, unstructured state space. Hence, it is possible to handle more complex systems. From our presentation it will be clear that the techniques also immediately apply to coloured Petri nets [4, 5] and other forms of high level Petri nets [1, 6]. This is very important since most practical modelling and analysis are performed by means of high level Petri nets. By presenting the techniques in terms of PT nets we reduce the level of technical details. The generalization to high level Petri nets is rather straightforward. The modular Petri ....

Reisig, W. (1991) Petri nets and algebraic specifications. Theoret. Comput. Sci., 80, 1--34. Also in Jensen, K. and Rozenberg, G. (eds) (1991) High-level Petri Nets: Theory and Application, pp. 137--170. Springer.

....some limitations of this object based formalism. Notions of class, inheritance as well as subtyping have therefore been introduced. This version, called CO OPN 2 [BB95] is based upon two underlying formalisms: order sorted algebras [GM92] for data structure matters, and the algebraic nets [Rei91] for the operational and concurrent aspects. In CO OPN 2, classes are object templates described by a special kind of algebraic nets, while objects are net instances of these classes. A specific aspect of CO OPN 2 is that it introduces subtyping and distinguishes it from inheritance. ....

Wolfgang Reisig. Petri nets and algebraic specifications. In Theoretical Computer Science, volume 80, pages 1--34. Elsevier, 1991.

....in Algebraic Nets Ekkart Kindler and Hagen Volzer Humboldt Universitat zu Berlin Institut fur Informatik D 10099 Berlin Germany Abstract. Algebraic Petri nets as defined by Reisig [15] lack a feature for modelling distributed network algorithms, viz. flexible arcs. In this paper we equip algebraic Petri nets with flexible arcs and we call the resulting extension algebraic system nets. We demonstrate that algebraic system nets are better suited for modelling distributed ....

....are special cases of a simulation. Still, a simulation can be verified in the same style as classical place invariants of algebraic Petri nets. Keywords: Algebraic Petri nets, flexible arcs, place invariants, verification techniques. Introduction Algebraic Petri nets as proposed by Reisig [15] lack a feature which is important for modelling distributed network algorithms: Arcs with flexible throughput flexible arcs for short are not allowed. We will motivate the use and the necessity of flexible arcs by help of an example. Then, we formally introduce a generalized version of ....

[Article contains additional citation context not shown here]

W. Reisig. Petri nets and algebraic specifications. Theoretical Comput. Sci., 80:1-- 34, May 1991.

....Object Oriented Petri Nets) is a specification language designed for the specification and the modeling of large concurrent systems. The two underlying formalisms of CO OPN 2 are the algebraic specifications and the Petri nets which are combined in a way that is similar to algebraic nets [Rei91] The former is used to describe the data structures and the functional aspects of a system, while the latter serves to model its concurrent features. However, both these formalisms are not suitable to specify in the large . To compensate for the lack of structuring capabilities in the Petri ....

Wolfgang Reisig. Petri nets and algebraic specifications. In Theoretical Computer Science, volume 80, pages 1--34. Elsevier, 1991.

....we present in details the methodology by applying it to the chosen distributed application. 2. The CO OPN 2 specification formalism CO OPN 2 [3] is an hybrid specification formalism based on algebraic specifications [6] and Petri nets that are combined in a way that is similar to algebraic nets [5]. Algebraic specifications are used to describe the data structures and the functional aspects of a system, while Petri nets allow to model the system s concurrent features. To compensate for algebraic Petri nets lack of structuring capabilities, CO OPN 2 provides a structuring mechanism based on ....

....any moment; 2] A user may add new integers into the system, at any moment, between his entering time and his exit time; 3] At any moment, the application can give a partial view of the state of the multiset; 4] A user may exit the system provided he has entered it. State and internal behavior: [5] The integers entered by the users are stored in a multiset; 6] The application realizes the sum of all the integers entered by all the users; 7] The sum is performed by chemical reactions according to the Gamma paradigm; 8] A chemical reaction removes two integers from the multiset, adds them ....

Wolfgang Reisig. Petri nets and algebraic specifications. In Theoretical Computer Science, volume 80, pages 1-- 34. Elsevier, 1991.

....to assess concerning the validation of properties during a reverse engineering process. 2. The CO OPN 2 specification formalism CO OPN 2 [3] is an hybrid specification formalism based on algebraic specifications [11] and Petri nets which are combined in a way that is similar to algebraic nets [9]. Algebraic specifications are used to describe the data structures and the functional aspects of a system, while Petri nets allow to model the system s concurrent features. To compensate for algebraic Petri nets lack of structuring capabilities, COOPN 2 provides a structuring mechanism based ....

.... in a multiset; 6] The application computes the sum of all the integers entered by all the users; 7] The sum is performed by chemical reactions according to the Gamma paradigm; 8] A chemical reaction removes two integers from the multiset, adds them up, and inserts the sum into the multiset; [9] There is only one type of chemical reactions, but several of them can occur simultaneously and concurrently on the multiset; 10] A chemical reaction may occur as soon as the state of the multiset is such that the chemical reaction can occur, i.e. as soon as there are at least two integers in the ....

Wolfgang Reisig. Petri nets and algebraic specifications. In Theoretical Computer Science, volume 80, pages 1--34. Elsevier, 1991.

....of the Java programming language are specified with COOPN 2. 4 Chapter 2 The CO OPN 2 Specification Formalism 2. 1 Concepts CO OPN 2 is an hybrid specification formalismbased on algebraic specifications [16] and Petri nets which are combined in a way that is similar to algebraic nets [13]. The former is used to describe the data structures and the functional aspects of a system, while the latter allows to model the system s concurrent features. However, both these formalisms are not suitable to specify in the large . To compensate for Petri nets lack of structuring capabilities, ....

Wolfgang Reisig. Petri nets and algebraic specifications. In Theoretical Computer Science, volume 80, pages 1--34. Elsevier, 1991.

....been presented. For example, combinations of an algebraic specification language with a process calculus: other than LOTOS, we have PSF, 13, 14] a combination of a process calculus similar to ACP with ASF (Algebraic Specification Formalism) 4] Petri nets [17] many proposals see, e.g. [18, 2, 6, 23]; statecharts [9] see in [16] a combination obtained following the method proposed here. But, there are also combinations using Z for the data part, for example with statecharts [5, 24] and with an object oriented language as Object Z [19] On the other hand, fixing some (even powerful) ....

W. Reisig. Petri Nets and Algebraic Specifications. T.C.S., 80:1--34, 1991.

....arcs, and transitions in high level Petri nets. Some of these languages are database language oriented [Horndasch et al. 1985; Richter and Durchholz 1992; Sibertin Blanc 1986] logic oriented [Genrich and Lautenbach 1981] algebraic [Battiston et al. 1988; Billington 1989; Kramer 1987; Reisig 1991], programming language oriented [Albert et al. 1989; Baldassari and Bruno 1988] For many of these languages a formal semantics has not been provided, and in contrast to our Filter Table formalism none of them matches all of the properties discussed at the end of Section 4. Our concept ....

REISIG, W. 1991. Petri nets and algebraic specifications. Theor. Comput. Sci. 80, 1--34.

....overcome some limitations of this object based formalism. Notions of class, inheritance as well as subtyping have therefore been introduced. This version, called CO OPN 2 [4] is based upon two underlying formalisms: order sorted algebras [10] for data structure matters, and the algebraic nets [16], for the operational and concurrent aspects. This work has been sponsored partially by the Esprit Long Term Research Project 20072 Design for Validation (DeVa) with the financial support of the OFES (Office F ed eral de l Education et de la Science) and by the Swiss National Science ....

Wolfgang Reisig. Petri nets and algebraic specifications. In Theoretical Computer Science, volume 80, pages 1--34. Elsevier, 1991.

.... mention the general models of concurrency including data structures, algebraic specification of concurrency [AR93] dynamic data types [Reg93] and objects and temporal logic [FM90] In the particular field of Petri nets related with HAP nets, we have High Level Petri nets [JR91] Algebraic Nets [Vau87, Rei91], Structured Algebraic nets [BCM88] More recently, some extensions of Petri nets including object orientation features have appeared [BP90, BC93, Lak94, SB94] The paper is organized as follows. In the next section we introduce the CO OPN 2 syntax by means of an example. Then, Hierarchical ....

....language combined with Petri Nets. More precisely, the CO OPN objects are interconnected modular entities described by algebraic nets. In fact, CO OPN is based on two simple and elegant concepts, algebraic data types [EM85] and Petri nets [Rei85] gathered into a more general model: algebraic nets [Vau87, Rei91]. Although algebraic nets are an important improvement of Petri nets, they are quite unsuitable when faced large problems. Therefore, some facilities have been included in the CO OPN model such as genericity, standard constructors on data types and structuring capabilities. Subtyping, a major ....

[Article contains additional citation context not shown here]

Wolfgang Reisig. Petri nets and algebraic specifications. In Theoretical Computer Science, volume 80, pages 1--34. Elsevier, 1991.

....in order to show how to use the CO OPN 2 specification language in the development of real distributed systems. 2 CO OPN 2 PRINCIPLES The two underlying formalisms of CO OPN 2 are the algebraic specifications and the Petri nets which are combined in a way that is similar to algebraic nets [11]. The former is used to describe the data structures and the functional aspects of a system, while the latter serves to model its concurrent features. However, both these formalisms are not suitable to specify in the large . To compensate for the lack of structuring capabilities in the Petri ....

Wolfgang Reisig. Petri nets and algebraic specifications. In Theoretical Computer Science, volume 80, pages 1--34. Elsevier, 1991.

....who have shown that it is necessary to extend the model of concurrency, in association with object orientation, in order to model real (distributed) systems. Thus, the idea of extending concurrency models has generated many different approaches. The High Level Petri Net approach (algebraic nets [Vau87, Rei91], LOOPN [Lak94] the Cooperative Nets (CN) SB94] the POT and POP s approaches [ELR90] OBJ SA [BCM88] CLOWN [BC93] the O O AHL approach [Rib94] the process logic approach (with LOTOS) the temporal logic approach [FM90] and our approach (structured algebraic nets) called CO OPN [BG91] 4 ....

Wolfgang Reisig. Petri nets and algebraic specifications. In Theoretical Computer Science, volume 80, pages 1--34. Elsevier, 1991.

....Object Oriented Petri Nets) is a specification language designed for the specification and the modeling of large concurrent systems. The two underlying formalisms of CO OPN 2 are the algebraic specifications and the Petri nets which are combined in a way that is similar to algebraic nets [Rei91] The former is used to describe the data structures and the functional aspects of a system, while the later serves to model its concurrent features. For the sake of homogeneity regarding the notion of subtyping, order sorted algebraic specifications [GM92] have been adopted for the description ....

Wolfgang Reisig. Petri nets and algebraic specifications. In Theoretical Computer Science, volume 80, pages 1--34. Elsevier, 1991.

....specification language called CO OPN 2 (Concurrent Object Oriented Petri Nets) BB94, BB95] the successor of CO OPN [BG91] in which some object oriented notions were poorly implemented. The CO OPN 2 language is based upon two formalisms: order sorted algebras [GM89] and algebraic nets [Rei91]. The former formalism is used to describe the data structure aspects, while the latter stands for the behavioral and concurrent aspects of the objects which compose the systems. The language deals with the major object oriented notions such as the notion of encapsulated entities or objects, the ....

Wolfgang Reisig. Petri nets and algebraic specifications. In Theoretical Computer Science, volume 80, pages 1--34. Elsevier, 1991.

....Incremental Test generation Final system Analysis Simulation Tests 2 The specification language: CO OPN 2. 1 Basic ideas The CO OPN specification language is based on two elegant concepts, Algebraic data types and Petri nets, which are merged into a more general model Algebraic nets [22]. In order to express efficiently certain operations on large instances, the standard constructors on data types, structuring capabilities and the genericity principle (both for objects and algebraic data types) are also included in CO OPN. 2.2 Concepts The formal model is based on an approach ....

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

....Petri Nets) is a specification language designed for the specification and the modeling of large concurrent systems. The two underlying formalisms of CO OPN are the algebraic specifications and the Petri nets which are combined in a way that is similar to the combination of algebraic nets [Rei91]. The first formalism is used to describe the data structures and the functional aspects of a system, while the second serves to model its operational and concurrent features. However, both these formalisms are not suitable to specify in the large . To compensate for the lack of structuring ....

....are not necessarily related by sub typing. Both of these relationships between classes must be explicitly expressed. 3.7 Other approaches The other approaches which may be compared to CO OPN 2 may be categorized in the High Level Petri Net class of models. These include algebraic nets [Rei91], OPN [Lak95] Cooperative Nets [SB94] and CLOWN [BCC95] among others. All these models are based upon the Petri nets as well as upon some formalisms which vehicle the data structures aspects. Moreover, the object oriented paradigm has been adopted by all these formalisms. 4 Cooperative diagram ....

Wolfgang Reisig. Petri nets and algebraic specifications. In Theoretical Computer Science, volume 80, pages 1--34. Elsevier, 1991.

....Object Oriented Petri Nets) is a specification language designed for the specification and the modeling of large concurrent systems. The two underlying formalisms of CO OPN 2 are the algebraic specifications and the Petri nets which are combined in a way that is similar to algebraic nets [Reisig 1991]. The former is used to describe the data structures and the functional aspects of a system, while the latter serves to model its concurrent features. However, both these formalisms are not suitable to specify in the large . To compensate for the lack of structuring capabilities in the Petri ....

Wolfgang Reisig. Petri Nets and Algebraic Specifications. In Theoretical Computer Science, volume 80, pages 1--34. Elsevier, 1991.

....to assess concerning the validation of properties during a reverse engineering process. 2. The CO OPN 2 specification formalism CO OPN 2 [4] is an hybrid specification formalism based on algebraic specifications [14] and Petri nets which are combined in a way that is similar to algebraic nets [10]. Algebraic specifications are used to describe the data structures and the functional aspects of a system, while Petri nets allow to model the system s concurrent features. To compensate for algebraic Petri nets lack of structuring capabilities, CO OPN 2 provides a structuring mechanism based on ....

.... chemical reactions according to the Gamma paradigm; 8] A chemical reaction removes two integers from the multiset, adds them up, and inserts the sum into the multiset; 9] There is only one type of chemical reactions, but several of them can occur simultaneously and concurrently on the multiset; [10] A chemical reaction may occur as soon as the state of the multiset is such that the chemical reaction can occur, i.e. as soon as there are at least two integers in the multiset. 3.2. The Java program P The Java program, P, of the distributed Gamma like addition follows a Java applet based ....

Wolfgang Reisig. Petri nets and algebraic specifications. In Theoretical Computer Science, volume 80, pages 1--34. Elsevier, 1991.

....component, which is the fundamental building block of a TOPnet system. As it is essentially a time extension of the OBJSA component, which is based on algebraic specification, it has a strong algebraic flavour. For more detailed information on algebraic nets and OBJSA nets, refer to the works of Reisig (1991) and Battiston et al. 1988) respectively. We first recall some fundamentals of algebraic specifications, according to Reisig (1991) A signature Sigma = S ; OP) consists of a set S of sorts and of a family OP = OPw ;s ) s2S ;s2S of operation symbols. A Sigma algebra A = S A ; OPA ) ....

....which is based on algebraic specification, it has a strong algebraic flavour. For more detailed information on algebraic nets and OBJSA nets, refer to the works of Reisig (1991) and Battiston et al. 1988) respectively. We first recall some fundamentals of algebraic specifications, according to Reisig (1991). A signature Sigma = S ; OP) consists of a set S of sorts and of a family OP = OPw ;s ) s2S ;s2S of operation symbols. A Sigma algebra A = S A ; OPA ) consists of a family SA = A s ) s2S of domains and a family OPA = NA ) N2OP of operations NA : A s 1 Theta : Theta A sn A s for ....

[Article contains additional citation context not shown here]

Reisig, W. (1991), `Petri nets and algebraic specifications', Theoretical Comput. Sci. 80, 1--34.

....values to the variables. The marking resulting from an occurrence is represented by an expression containing the variables of the involved transition. In [78] the ideas of parameterised reachability graphs were transferred to another class of High level Petri Nets, the Algebraic Petri Nets [75]. To the knowledge of this author, no implementation of the parameterised reachability graph method has been published, and a conclusion of [79] is that the technical details are quite difficult to manage. 4.2 Well formed Coloured Nets Well formed Coloured Nets [15] resemble CP nets, but have ....

W. Reisig. Petri Nets and Algebraic Specifications. In K. Jensen and G. Rozenberg, editors, High-level Petri Nets, Theory and Application. Springer-Verlag, 1991.

....Petri Nets) specification language [6] 7] and the associated development tool called SANDS (Structured Algebraic Nets Development System) 8] 9] CO OPN is directed towards specification of complex distributed systems. The specification language is based on hierarchical algebraic Petri nets [21], where the Petri nets are used to model operational and concurrent aspects. The object notion of CO OPN serves as a structuring means, and naturally captures the concurrent aspects of a model. Each CO OPN object is a Petri net, which is connected to other objects through transaction oriented ....

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

....we present in details the methodology by applying it to the chosen distributed application. 2 The CO OPN 2 specification formalism CO OPN 2 [3] is an hybrid specification formalism based on algebraic specifications [8] and Petri nets that are combined in a way that is similar to algebraic nets [6]. Algebraic specifications are used to describe the data structures and the functional aspects of a system, while Petri nets allow to model the system s concurrent features. To compensate for algebraic Petri nets lack of structuring capabilities, CO OPN 2 provides a structuring mechanism based on ....

....moment, between his entering time and his exit time; 3] At any moment, the application can give a partial view of the state of the multiset; 4] A user may exit the system provided he has entered it. State and internal behavior: 5] The integers entered by the users are stored in a multiset; [6] The application realizes the sum of all the integers entered by all the users; 7] The sum is performed by chemical reactions according to the Gamma paradigm; 8] A chemical reaction removes two integers from the multiset, adds them up, and inserts the sum into the multiset; 9] There is only ....

Wolfgang Reisig. Petri nets and algebraic specifications. In Theoretical Computer Science, volume 80, pages 1--34. Elsevier, 1991.

....y) return the set of variables of sort 2Tuple N;D appearing as the components of the formal sum. Then, for every a 2 P [ T, let: ffi a = f(b; l) j b 2 ffl a; l 2 var( b; a) g and a ffi = f(b; l) j b 2 a ffl ; l 2 var( a; b) g Recall that for t 2 T , similar to the definitions given in [17], t is enabled under a particular token assignment fi. Definition 4.2 Given a; b 2 T, for all (p; l) 2 ffi a and (p 0 ; l 0 ) 2 ffi b and for all assignments fi, a is independent of b i.e. a j b , fi(l) 6= fi(l 0 ) In other words, for two transitions to be independent, they are ....

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

....Petri Nets) is a specification language designed for the specification and the modeling of large concurrent systems. The two underlying formalisms of CO OPN are the algebraic specifications and the Petri nets which are combined in a way that is similar to the combination of algebraic nets [Rei91]. The first formalism is used to describe the data structures and the functional aspects of a system, while the second serves to model its operational and concurrent features. However, both these formalisms are not suitable to specify in the large . To compensate for the lack of structuring ....

....are not necessarily related by sub typing. Both of these relationships between classes must be explicitly expressed. 3.7 Other Approaches The other approaches which may be compared to CO OPN 2 may be categorized in the High Level Petri Net class of models. These include algebraic nets [Rei91], OPN [Lak95] Cooperative Nets [SB94] and CLOWN [BCC95] among others. All these models are based upon the Petri nets as well as upon some formalisms which vehicle the data structures aspects. Moreover, the object oriented paradigm has been adopted by all these formalisms. 4 Cooperative Diagram ....

Wolfgang Reisig. Petri nets and algebraic specifications. In Theoretical Computer Science, volume 80, pages 1--34. Elsevier, 1991.

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Wolfgang Reisig. Petri nets and algebraic specifications. Theor. Comput. Sci., 80(1):1--34, 1991.

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W. Reisig. Petri Nets and Algebraic Specifications. T.C.S., 80:1--34, 1991.

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