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39
U.: Adhesive HighLevel Replacement Categories and Systems
 Proceedings of ICGT 2004. Volume 3256 of LNCS
, 2004
"... Abstract. 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 Soboci ..."
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Cited by 28 (8 self)
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Abstract. 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. 1
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.
Transactions and ZeroSafe Nets
 Advances in Petri Nets: Unifying Petri Nets, Lect. Notes in Comput. Sci. 2128
, 2001
"... When employing Petri nets to model distributed systems, one must be aware that the basic activities of each component can vary in duration and can involve smaller internal activities, i.e., that transitions are conceptually refined into transactions. We present an approach to the modeling of transac ..."
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Cited by 14 (8 self)
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When employing Petri nets to model distributed systems, one must be aware that the basic activities of each component can vary in duration and can involve smaller internal activities, i.e., that transitions are conceptually refined into transactions. We present an approach to the modeling of transactions based on zerosafe nets. They extend ordinary pt nets with a simple mechanism for transition synchronization. We show that the net theory developed under the two most diffused semantic interpretations (collective token and individual token philosophies) can be uniformly adapted to zerosafe nets. In particular, we show that each zerosafe net has associated two pt nets which represent the abstract counterparts of the modeled system according to the two philosophies. We show several applications of the framework, a distributed interpreter for zs nets based on classical net unfolding (here extended with a commit rule) and discuss some extensions to other net flavours.
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.
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 11 (7 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...
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 11 (8 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, ...
Safety Preserving Transformations of Coloured Petri Nets
, 2000
"... In this paper a formal technique for refining Coloured Petri Nets within the software development process is introduced. This technique  called rulebased refinement  is based on rules and transformations of Coloured Petri Nets preserving safety properties in the sense of [MP92]. First steps tow ..."
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Cited by 5 (3 self)
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In this paper a formal technique for refining Coloured Petri Nets within the software development process is introduced. This technique  called rulebased refinement  is based on rules and transformations of Coloured Petri Nets preserving safety properties in the sense of [MP92]. First steps towards this approach have been suggested for algebraic highlevel nets [PGE98] and place/transition nets [PGH99] already. The results presented here exceed the previous in the way safety properties can be preserved or even introduced. The proposed rulebased refinement is applied to the development of a traffic control system for illustration. The presented results have been achieved on a more abstract level of typed highlevel abstract Petri nets [Pad99a] and transferred to Coloured Petri Nets via instantiation.
The Expert View of the "Petri Net Baukasten"
 Int. Colloquium on Petri Net Technologies for Modelling Communication Based Systems. Fraunhofer Gesellschaft ISST
, 1999
"... As part of the Petri Net Baukasten' [Pad99b] the Expert View presents mathematical concepts and results of Petri net theory in a structured and application oriented way. Consistent formal Petri net techniques and transformations between these are main issues. We introduce the notions of formal ..."
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Cited by 5 (2 self)
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As part of the Petri Net Baukasten' [Pad99b] the Expert View presents mathematical concepts and results of Petri net theory in a structured and application oriented way. Consistent formal Petri net techniques and transformations between these are main issues. We introduce the notions of formal Petri net techniques, abstract Petri net frames, instantiations, and transformations. These notions are specified by schemes which are used to represent specic pieces of Petri net theory known from literature. Furthermore, the Expert View presents explicit formal descriptions of concepts described semiformally in the Common Base [Deh99].
Concepts and Requirements for Transformations within Petri Net Based Process Models
 5 th World Conference on Integrated Design and Process Technology, Special Session on Model Integration, 2000. CDROM
, 2000
"... We propose transformations in order to support Petri net based process models for software development. Our concept of transformation comprises changes of the Petri net formalism, called net class transformation and changes of Petri nets, called model transformation. In this paper transformations ar ..."
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Cited by 4 (1 self)
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We propose transformations in order to support Petri net based process models for software development. Our concept of transformation comprises changes of the Petri net formalism, called net class transformation and changes of Petri nets, called model transformation. In this paper transformations are introduced on a conceptional level and related to existing notions in literature. Based on this concept requirements and first results for a the theory of transformations are stated. They comprise preservation of system properties, compatibility of transformations with structuring techniques, consistency between Petri net models and their integration.