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48
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 36 (18 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...
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 27 (14 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.
Adhesive highlevel replacement categories and systems
, 2004
"... Adhesive highlevel replacement (HLR) categories and systems are introduced as a new categorical framework for graph transformation in a broad sense, which combines the wellknown concept of HLR systems with the new concept of adhesive categories introduced by Lack and Sobociński. In this paper we s ..."
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Cited by 25 (6 self)
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Adhesive highlevel replacement (HLR) categories and systems are introduced as a new categorical framework for graph transformation in a broad sense, 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 ad hoc to generalize some basic results from the category of graphs to highlevel structures, are valid already in adhesive HLR categories. As a main new result in a categorical framework we show the Critical Pair Lemma for local confluence of transformations. Moreover we present a new version of embeddings and extensions for transformations in our framework of adhesive HLR systems.
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 19 (4 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 17 (6 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.
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 15 (13 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.
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 11 (5 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.
Requirements Engineering Of A Medical Information System Using RuleBased Refinement Of Petri Nets
 Proc. Integrated Design and Process Technology
, 1996
"... This paper is concerned with the application of a formal technique to software engineering. In this case study we have used rulebased refinement of algebraic highlevel nets for the requirements engineering of a medical information system. We outline the basic ideas of rulebased refinement and dis ..."
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Cited by 10 (7 self)
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This paper is concerned with the application of a formal technique to software engineering. In this case study we have used rulebased refinement of algebraic highlevel nets for the requirements engineering of a medical information system. We outline the basic ideas of rulebased refinement and discuss how this technique is applied to the development from actual state analysis to functional essence. INTRODUCTION The main idea of requirements engineering in general is the analysis of the system leading to a documentation of the actual state and a transformation of the actual state to the functional essence of the corresponding system (see [DeM78, Dav90, Huß93]). Hence, requirements engineering is a stepwise abstraction of the actual state leading to the functional essence. In this paper we start with a documentation of the actual state of an information system by highlevel Petri nets [JR91, Jen95], and more precisely by algebraic highlevel nets in the spirit of [Vau86, KS91, Rei91, ...
Categorical Approach to Horizontal Structuring and Refinement of HighLevel Replacement Systems
 APPLIED CATEGORICAL STRUCTURES
, 1998
"... Based on the wellknown theory of highlevel replacement systems  a categorical formulation of graph grammars  we present new results concerning refinement of highlevel replacement systems. Motivated by Petri nets, where refinement is often given by morphisms, we give a categorical notion of re ..."
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Cited by 10 (6 self)
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Based on the wellknown theory of highlevel replacement systems  a categorical formulation of graph grammars  we present new results concerning refinement of highlevel replacement systems. Motivated by Petri nets, where refinement is often given by morphisms, we give a categorical notion of refinement. This concept is called Qtransformations and is established within the framework of highlevel replacement systems. The main idea is to supply rules with an additional morphism, which belongs to a specific class Q of morphisms. This leads to the new notions of Qrules and Qtransformations. Moreover, several concepts and results of highlevel replacement systems are extended to Qtransformations. These are sequential and parallel transformations, union, and fusion, based on different colimit constructions. The main results concern the compatibility of these constructions with Qtransformations that is the corresponding theorems for usual transformations are extended to Qtransform...
Horizontal and Vertical Structuring Techniques for Statecharts
, 1997
"... In this paper we present an algebraic approach to statecharts as they are used in the Statemate tool in the style of "PetriNets are Monoids" for placetransition nets developed by Meseguer and Montanari. We apply the framework of highlevelreplacement systems, a categorical generalization of g ..."
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Cited by 7 (5 self)
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In this paper we present an algebraic approach to statecharts as they are used in the Statemate tool in the style of "PetriNets are Monoids" for placetransition nets developed by Meseguer and Montanari. We apply the framework of highlevelreplacement systems, a categorical generalization of graph transformation systems, in order to de#ne union as horizontal as well as transformation and re#nementasvertical structuring techniques for statecharts. The #rst main result shows compatibility of union and transformation in a suitable category of statecharts. We present an algorithm for the computation of all transitions enabled within one step. The second main result shows the correctness of this algorithm. We de#ne re#nement morphisms for statecharts, which allow re#nement of arbitrary states, in contrast to concepts in the literature where only basic and root states are subject of re#nement. The third main result shows that re#nement morphisms are compatible with the behavio...