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89
Abstract Petri Nets as a Uniform Approach to HighLevel Petri Nets
, 1998
"... In the area of Petri nets, many different developments have taken place within the last 30 years, in academia as well as in practice. For an adequate use in practice, a coherent and application oriented combination of various types and techniques for Petri nets is necessary. In order to attain ..."
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Cited by 41 (21 self)
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In the area of Petri nets, many different developments have taken place within the last 30 years, in academia as well as in practice. For an adequate use in practice, a coherent and application oriented combination of various types and techniques for Petri nets is necessary. In order to attain a formal basis for different classes of Petri nets we introduce the concept of abstract Petri nets. The essential point of abstract Petri nets is to allow different kinds of net structures as well as the combination of various kinds of data types. This means that in abstract Petri nets the data type and the net structure part can be considered as abstract parameters which can be instantiated to different concrete net classes. We show that several net classes, like place/transition nets, elementary nets, Sgraphs, algebraic highlevel net...
Weak Adhesive HighLevel Replacement Categories and Systems: A Unifying . . .
, 2006
"... Adhesive highlevel replacement (HLR) systems have been recently introduced as a new categorical framework for graph tranformation in the double pushout (DPO) approach. They combine the wellknown concept of HLR systems with the concept of adhesive categories introduced by Lack and Sobociński. Wh ..."
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Cited by 34 (11 self)
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Adhesive highlevel replacement (HLR) systems have been recently introduced as a new categorical framework for graph tranformation in the double pushout (DPO) approach. They combine the wellknown concept of HLR systems with the concept of adhesive categories introduced by Lack and Sobociński. While graphs, typed graphs, attributed graphs and several other variants of graphs together with corresponding morphisms are adhesive HLR categories, such that the categorical framework of adhesive HLR systems can be applied, this has been claimed also for Petri nets. In this paper we show that this claim is wrong for place/transition nets and algebraic highlevel nets, although several results of the theory for adhesive HLR systems are known to be true for the corresponding Petri net transformation systems. In fact, we are able to define a weaker version of adhesive HLR categories, called weak adhesive HLR categories, which is still sufficient to show all the results known for adhesive HLR systems. This concept includes not only all kinds of graphs mentioned above, but also place/transition nets, algebraic highlevel nets and several other kinds of Petri nets. For this reason weak adhesive HLR systems can be seen as a unifying framework for graph and Petri net transformations.
Highlevel nets with nets and rules as tokens
 In Proc. of ICATPN 2005
, 2005
"... Abstract. HighLevel net models following the paradigm “nets as tokens” have been studied already in the literature with several interesting applications. In this paper we propose the new paradigm “nets and rules as tokens”, where in addition to nets as tokens also rules as tokens are considered. Th ..."
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Cited by 33 (14 self)
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Abstract. HighLevel net models following the paradigm “nets as tokens” have been studied already in the literature with several interesting applications. In this paper we propose the new paradigm “nets and rules as tokens”, where in addition to nets as tokens also rules as tokens are considered. The rules can be used to change the net structure. This leads to the new concept of highlevel net and rule systems, which allows to integrate the token game with rulebased transformations of P/Tsystems. The new concept is based on algebraic highlevel nets and on the main ideas of graph transformation systems. We introduce the new concept with the case study “House of Philosophers”, a dynamic extension of the wellknown dining philosophers. In the main part we present a basic theory for rulebased transformations of P/Tsystems and for highlevel nets with nets and rules as tokens leading to the concept of highlevel net and rule systems.
Horizontal and Vertical Structuring of Typed Graph Transformation Systems
, 1996
"... this paper we concentrate on structuring and refinement concepts for graph transformation systems. Conceptually, we distinguish between two kinds of structuring. We speak of horizontal structuring if a large specification is obtained by combining and modifying smaller ones, possibly sharing some com ..."
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Cited by 32 (19 self)
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this paper we concentrate on structuring and refinement concepts for graph transformation systems. Conceptually, we distinguish between two kinds of structuring. We speak of horizontal structuring if a large specification is obtained by combining and modifying smaller ones, possibly sharing some common parts. Instead, if we consider the relationship between a more abstract and a more concrete version of the same specification, or between a specification and its implementation, we speak of vertical structuring.
Compositional Semantics for Open Petri Nets based on Deterministic Processes
, 2001
"... In order to model the behaviour of open concurrent systems by means of Petri nets, we introduce open Petri nets, a generalization of the ordinary model where some places, designated as open, represent an interface of the system towards the environment. Besides generalizing the token game to reflect ..."
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Cited by 29 (7 self)
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In order to model the behaviour of open concurrent systems by means of Petri nets, we introduce open Petri nets, a generalization of the ordinary model where some places, designated as open, represent an interface of the system towards the environment. Besides generalizing the token game to reflect this extension, we define a truly concurrent semantics for open nets by extending the GoltzReisig process semantics of Petri nets. We introduce a composition operation over open nets, characterized as a pushout in the corresponding category, suitable to model both interaction through open places and synchronization of transitions. The deterministic process semantics is shown to be compositional with respect to such composition operation. If a net Z 3 results as the composition of two nets Z 1 and Z 2 , having a common subnet Z 0 , then any two deterministic processes of Z 1 and Z 2 which "agree" on the common part, can be "amalgamated" to produce a deterministic process of Z 3 . Vice versa, any deterministic process of Z 3 can be decomposed into processes of the component nets. The amalgamation and decomposition operations are shown to be inverse to each other, leading to a bijective correspondence between the deterministic processes of Z 3 and pair of deterministic processes of Z 1 and Z 2 which agree on the common subnet Z 0 . Technically, our result is similar to the amalgamation theorem for datatypes in the framework of algebraic specification. A possible application field of the proposed constructions and results is the modeling of interorganizational workflows, recently studied in the literature. This is illustrated by a running example.
Compositional modeling of reactive systems using open nets
, 2001
"... In order to model the behaviour of open concurrent systems by means of Petri nets, we introduce open Petri nets, a generalization of the ordinary model where some places, designated as open, represent an interface of the system towards the environment. Besides generalizing the token game to reflect ..."
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Cited by 21 (9 self)
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In order to model the behaviour of open concurrent systems by means of Petri nets, we introduce open Petri nets, a generalization of the ordinary model where some places, designated as open, represent an interface of the system towards the environment. Besides generalizing the token game to reflect this extension, we define a truly concurrent semantics for open nets by extending the GoltzReisig process semantics of Petri nets. We introduce a composition operation over open nets, characterized as a pushout in the corresponding category, suitable to model both interaction through open places and synchronization of transitions. The process semantics is shown to be compositional with respect to such composition operation. Technically, our result is similar to the amalgamation theorem for datatypes in the framework of algebraic specifications. A possible application field of the proposed constructions and results is the modeling of interorganizational workflows, recently studied in the literature. This is illustrated by a running example.
Adhesive HighLevel Replacement Systems: A New Categorical Framework for Graph Transformation
, 2006
"... Adhesive highlevel replacement (HLR) systems are introduced as a new categorical framework for graph transformation in the double pushout (DPO) approach, which combines the wellknown concept of HLR systems with the new concept of adhesive categories introduced by Lack and Sobociński. In this pa ..."
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Cited by 20 (12 self)
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Adhesive highlevel replacement (HLR) systems are introduced as a new categorical framework for graph transformation in the double pushout (DPO) approach, which combines the wellknown concept of HLR systems with the new concept of adhesive categories introduced by Lack and Sobociński. In this paper we show that most of the HLR properties, which had been introduced to generalize some basic results from the category of graphs to highlevel structures, are valid already in adhesive HLR categories. This leads to a smooth categorical theory of HLR systems which can be applied to a large variety of graphs and other visual models. As a main new result in a categorical framework we show the Critical Pair Lemma for the local confluence of transformations. Moreover we present a new version of embeddings and extensions for transformations in our framework of adhesive HLR systems.
RuleBased Refinement of HighLevel Nets Preserving Safety Properties
 Fundamental approaches to Software Engineering
, 1998
"... The concept of rulebased modification developed in the area of algebraic graph transformations and highlevel replacement systems has recently shown to be a powerful concept for vertical stucturing of Petri nets. This includes lowlevel and highlevel Petri nets, especially algebraic highlevel net ..."
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Cited by 16 (14 self)
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The concept of rulebased modification developed in the area of algebraic graph transformations and highlevel replacement systems has recently shown to be a powerful concept for vertical stucturing of Petri nets. This includes lowlevel and highlevel Petri nets, especially algebraic highlevel nets which can be considered as an integration of algebraic specifications and Petri nets. In a large case study rulebased modi cation of algebraic highlevel nets has been applied successfully for the requirements analysis of a medical information system. The main new result in this paper extends rulebased modification of algebraic highlevel nets such that it preserves safety properties formulated in terms of temporal logic. For software development based on rulebased modi cation of algebraic highlevel nets as a vertical development strategy this extension is an important new technique. It is called rulebased re nement. As a running example an important safety property of a medical information system is considered and is shown to be preserved under rulebased refinement.
RuleBased Refinement of Petri Nets: A Survey
 Advances in Petri Nets: Petri Net Technology for Communication Based Systems, volume 2472 of LNCS
"... Abstract. This contribution provides a thorough survey of our work on rulebased refinement. Rulebased refinement comprises the transformation of Petri nets using rules while preserving certain system properties. Petri net rules and transformations are expressed by morphisms and pushouts. This all ..."
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Cited by 15 (6 self)
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Abstract. This contribution provides a thorough survey of our work on rulebased refinement. Rulebased refinement comprises the transformation of Petri nets using rules while preserving certain system properties. Petri net rules and transformations are expressed by morphisms and pushouts. This allows an abstract formulation of our notions independent of a specific Petri net class, as place/transition nets, elementary nets, predicate/transition nets etc. Hence, it is adequate to consider our approach as rulebased refinement of Petri nets in general. We have presented various results in recent years at different conferences. So this contribution gives an overview of our work in a compact form leaving out the technical details.
A Uniform Approach to Petri Nets
 FOUNDATIONS OF COMPUTER SCIENCE: POTENTIAL  THEORY  COGNITION. SPRINGER, LNCS 1337
, 1997
"... The new concept of parameterized net classes is introduced in order to allow a uniform presentation of different kinds of Petri net classes. By different actualizations of the net structure parameter and the data type parameter we obtain several wellknown net classes, like elementary nets, placetra ..."
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Cited by 12 (6 self)
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The new concept of parameterized net classes is introduced in order to allow a uniform presentation of different kinds of Petri net classes. By different actualizations of the net structure parameter and the data type parameter we obtain several wellknown net classes, like elementary nets, placetransition nets, coloured Petri nets, predicate /transition nets, and algebraic highlevel nets, as well as several interesting new classes of low and highlevel nets. While the concept of parameterized net classes is defined on a purely set theoretical level, we also sketch an extended concept of universal parameterized net classes taking into account also morphisms and universal properties in the sense of category theory. The extended concept, presented in a sperate paper, leads to a uniform theory of constructions and compatibility results concerning union and fusion of nets for different types of net classes.