High-level Replacement Systems Research Articles

Modeling dynamic reconfigurations in Reo using high-level replacement systems

Reo is a channel-based coordination language, wherein circuit-like connectors model and implement interaction protocols in heterogeneous environments that coordinate components or services. Connectors are constructed from primitive channels and can be reconfigured dynamically. Reconfigurations can even execute within a pending I/O transaction. In this article, we formally model and analyze dynamic reconfigurations and show how running coordinators can be reconfigured without the cooperation of their engaged components. We utilize the theory of high-level replacement systems to model rule-based reconfigurations of connectors. This allows us to perform a complex reconfiguration as an atomic step and analyze it using formal verification techniques. Specifically, we formalize the structure of connectors as typed hypergraphs and use critical pair and state space analyses for verification of dynamic reconfigurations. We provide a full implementation of our approach in a framework that includes tools for the definition, analysis, and execution of reconfigurations, and is integrated with two execution engines for Reo. Our framework, moreover, integrates with the graph transformation tools AGG and GROOVE for formal analysis, as well as the Eclipse platform and standard web service technologies.

Parallelism and Concurrency in Adhesive High-Level Replacement Systems with Negative Application Conditions

The goal of this paper is the generalization of parallelism and concurrency results for adhesive High-Level Replacement (HLR) systems to adhesive HLR systems with negative application conditions. These conditions restrict the application of a rule by expressing that a specific structure should not be present before or after applying the rule to a certain context. Such a condition influences thus each rule application or transformation and therefore changes significantly the properties of the replacement system. The effect of negative application conditions on parallelism and concurrency in the replacement system is described in the generalization of the following results, formulated already for adhesive HLR systems without negative application conditions: Local Church-Rosser Theorem, Parallelism Theorem and Concurrency Theorem. These important generalized results will support the development of formal analysis techniques for adhesive HLR systems with negative application conditions.

Towards Algebraic High-Level Systems as Weak Adhesive HLR Categories

Adhesive high-level replacement (HLR) systems have been recently established as a suitable categorical framework for double pushout transformations based on weak adhesive HLR categories. Among different types of graphs and graph-like structures, various kinds of Petri nets and algebraic high-level (AHL) nets are interesting instantiations of adhesive HLR systems. AHL nets combine algebraic specifications with Petri nets to allow the modeling of data, data flow and data changes within the net.For the development and analysis of reconfigurable systems, not only AHL schemas based on an algebraic specification and AHL nets using an additional algebra should be considered, but also AHL systems which additionally include markings of nets.In this paper, we summarize the results for different kinds of AHL schemas and nets, and extend these results to AHL systems. The category of markings is introduced, which allows a general construction combining AHL nets with possible markings leading under certain properties to a weak adhesive HLR category.

Connector Rewriting with High-Level Replacement Systems

Reo is a language for coordinating autonomous components in distributed environments. Coordination in Reo is performed by circuit-like connectors, which are constructed from primitive channels with well-defined behavior. These channels are mobile, i.e. can be dynamically created and reconfigured at run-time. Based on these language features, we introduce a high-level transformation system for Reo. We show how transformations of Reo connectors can be defined using the theory of high-level replacement (HLR) systems. This leads to a powerful notion of dynamic connector reconfiguration in Reo. Moreover, the rewrite rules are naturally expressed in Reo's visual syntax for connectors.Applications of this framework are manifold, due to the generality of the field of coordination. In this paper we provide an example from the area of Service-oriented Computing.

Integration of Categorical Frameworks: Rule-Based Refinement and Hierarchical Composition for Components

The integration of two important categorical frameworks – namely adhesive High-Level Replacement (HLR) systems and the generic component concept– yields a categorical approach to component transformation and refinement. The generic component concept is shown to be an adhesive HLR category, so rules and transformations as well as the corresponding results are available. Moreover, the compatibility with the hierarchical component composition is provided. The extension to rule-based refinement requires additional property-preserving morphisms and yields property-preserving rules and transformations, i.e. refinements where compatibility with the hierarchical component composition again is achieved. The categorical framework is instantiated to typed algebraic high-level (AHL) nets and illustrated with an example of AHL net components.

Construction and Properties of Adhesive and Weak Adhesive High-Level Replacement Categories

As presented in Ehrig et al. (Fundamentals of Algebraic Graph Trans- formation, EATCS Monographs, Springer, 2006), adhesive high-level replacement (HLR) categories and systems are an adequate framework for several kinds of trans- formation systems based on the double pushout approach. Since (weak) adhesive HLR categories are closed under product, slice, coslice, comma and functor category constructions, it is possible to build new (weak) adhesive HLR categories from existing ones. But for the general results of transformation systems, as additional properties initial pushouts, binary coproducts compatible with a special morphism class M and a pair factorization are needed to obtain the full theory. In this paper, we analyze under which conditions these additional properties are preserved by the categorical constructions in order to avoid checking these properties explicitly.

Transformations of Petri Nets

The aim of this paper is an introduction to the area of Petri net transformations, a rule-based approach for dynamic changes of the net structure of Petri nets. This is especially important for the stepwise construction of Petri nets in the sense of the software development process in software engineering. The concept of Petri net transformations is based on that of graph transformations and high-level replacement systems and it is introduced within a small case study logistics.

High-level replacement units and their termination properties

Visual rewriting techniques, in particular graph transformations, are increasingly used to model transformations of systems specified through diagrammatic sentences. Several rewriting models have been proposed, differing in the expressivity of the types of rules and in the complexity of the rewriting mechanism; yet, for many of them, basic results concerning the formal properties of these models are still missing. In this paper, we give a contribution towards solving the termination problem for rewriting systems with external control mechanisms. In particular, we obtain results of more general validity by extending the concept of transformation unit to high-level replacement systems, a generalization of graph transformation systems. For high-level replacement units, we state and prove several abstract properties based on termination criteria. Then, we instantiate the high-level replacement systems by attributed graph transformation systems and present concrete termination criteria. We explore some types of rules and replacement units for which the criterion can be established. These are used to show the termination of some replacement units needed to express model transformations formalizing refactoring.

On Term Graphs as an Adhesive Category

The recent interest in bisimulation congruences for reduction systems, stimulated by the research on general (often graphical) frameworks for nominal calculi, has brought forward many proposals for categorical formalisms where relevant properties of observational equivalences could be auto- matically verified.Interestingly, some of these formalisms also identified suitable categories where the standard tools and techniques developed for the double-pushout approach to graph transformation [A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel and M. Löwe, Algebraic approaches to graph transformation I: Basic concepts and double pushout approach, in: G. Rozenberg, editor, Handbook of Graph Grammars and Computing by Graph Transformation, I: Foundations, World Scientific, 1997, pp. 163–246] could be recast, thus providing a valid alternative to the High-Level Replacement Systems paradigm [H. Ehrig, A. Habel, H.-J. Kreowski and F. Parisi-Presicce, Parallelism and concurrency in highlevel replacement systems, Mathematical Structures in Computer Science 1 (1991) 361–404].In this paper we consider the category of term graphs, and we prove that it (partly) fits in the general framework for adhesive categories, developed in [S. Lack, and P. Sobociński, Adhesive categories, in: I. Walukiewicz, editor, Foundations of Software Science and Computation Structures, Lect. Notes in Comp. Sci. 2987 (2004), pp. 273–288, P. Sobociński, “Deriving bisimulation congruences from reduction systems”, Ph.D. thesis, BRICS, Department of Computer Science, University of Aaurhus (2004)], extended in [H. Ehrig, A. Habel, J. Padberg and U. Prange, Adhesive high-level replacement categories and systems, in: G. Engels and F. Parisi-Presicce, editors, Graph Transformation, Lect. Notes in Comp. Sci. (2004)] and applied to reduction systems in [V. Sassone, and P. Sobociński, Congruences for contextual graph-rewriting, Technical Report RS-04-11, BRICS, Department of Computer Science, University of Aarhus (2004)]. The main technical achievement concerns the proof that the category of term graphs is actually quasi-adhesive, obtained by proving the existence of suitable Van Kampen squares.

Termination of High-Level Replacement Units with Application to Model Transformation

Visual rewriting techniques, in particular graph transformations, are increasingly used to model transformations of systems specified through diagrammatic sentences. Several rewriting models have been proposed, differing in the expressivity of the types of rules and in the complexity of the rewriting mechanism; yet basic results concerning the formal properties of these models are still missing for many of them. In this paper, we propose a contribution towards solving the termination problem for rewriting systems with external control mechanisms. In particular, we obtain results of more general validity by extending the concept of transformation unit to high-level replacement systems, a generalization of graph transformation systems. For high-level replacement units, we state and prove several abstract properties based on termination criteria. Then, we instantiate the high-level replacement systems by attributed graph transformation systems and present concrete termination criteria. These are used to show the termination of some replacement units needed to express model transformations as a consequence of software refactoring.

A component framework for system modeling based on high-level replacement systems

The aim of this paper is to present a generic component framework for system modeling that satisfies main requirements for component-based development in software engineering. In this sense, we have defined a framework that can be used, by providing an adequate instantiation, in connection with a large class of semi-formal and formal modeling techniques. Moreover, the framework is also flexible with respect to the connection of components, providing a compositional semantics of components. This means more precisely that the semantics of a system can be inferred from the semantics of its components. In contrast to other component concepts for data type specification techniques, our component framework is based on a generic notion of transformations. In particular, refinements and transformations are used to express intradependencies, between the export interface and the body of a component, and interdependencies, between the import and the export interfaces of different components. The generic component framework generalizes module concepts for different kinds of Petri nets and graph transformation systems proposed in the literature, and seems to be also suitable for visual modeling techniques, including parts of the UML, if these techniques provide a suitable refinement or transformation concept. In this paper the generic approach is instantiated in two steps. First to high-level replacement systems generalizing the transformation concept of graph transformations. In a second step it is further instantiated to low-level and high-level Petri nets. To show applicability we present sample components from a case study in the domain of production automation as proposed in a priority program of the German Research Council (DFG).

Basic Results for Two Types of High-Level Replacement Systems

Abstract The general idea of high-level replacement systems is to generalize the concept of graph transformation systems and graph grammars from graphs to all kinds of structures which are of interest in Computer Science and Mathematics. Within the algebraic approach of graph transformation this is possible by replacing graphs, graph morphisms, and pushouts (gluing) of graphs by objects, morphisms, and pushouts in a suitable category. Of special interest are categories for all kinds of labelled and typed graphs, hypergraphs, algebraic specifications and Petri nets. In this paper, we review the basic results for high-level replacement systems in the algebraic double-pushout approach in the symmetric case, where both rule morphisms belong to a distinguished class M . Moreover we present for the first time the asymmetric type of high-level replacement systems, where only the left rule morphism K → L belongs to M .

Preface: UNIGRA'03 - Uniform Approaches to Graphical Process Specification Techniques

This volume contains selected papers of the proceedings of the workshop on Uniform Approaches to Graphical Process Specification Techniques (UNIGRA'03). The workshop was held in Warsaw, Poland, on April 5 and 6, 2003, as a satellite event of the sixth European Joint Conference on Theory and Practice of Software (ETAPS 2003). The workshop continues the UNIGRA workshop in 2001 which has been a successful satellite event of ETAPS 2001.Workshop ObjectivesDue to the increasing amount of divergent formalisms, the main idea of the UNIGRA workshops is to bring together people working especially in the following three areas: •Low Level and High-Level Petri Nets•Graph Transformation and High-Level Replacement Systems•Visual Modeling Techniques including UMLIn each of these areas there is a large variety of different approaches, however, first attempts for uniform approaches have been made already. According to the main idea and in order to further stimulate the research in this important area, this volume presents some uniform approaches and further introduce unifying and comparative studies across the borders of the three and related areas.Workshop ProgramIn the first part, unifying approaches for low-level and high-level Petri nets are proposed:The contribution by Ehrig shows how the notions occurrence net and process can be generalized from low-level to high-level Petri nets, and studies the behavior and instantiations of this new view of processes for high-level nets.In his overview on new developments in the area of Petri net transformations for Software Engineering, Urbášek presents recent work on net model transformations and net class transformations. Both kinds of transformations are studied with regard to the preservation of system properties such as safety properties or liveness. The formalization of Petri net transformations is originally based on the theory of graph transformation.Padberg considers a case study (the call center of a phone company)which is modeled using Petri net modules for structuring the operational behavior of the system. The notion of Petri net modules was achieved by a transfer from the concepts of algebraic module specifications to the modeling of component-based systems by Petri nets.Desel, Juhás and Lorenz deal with the semantics of place/transition nets. The authors relate the process semantics based on partial orders (individual token semantics) to the collective token semantics by defining partial orders associated to process terms of place/transition nets.In the second part concerning graph transformation and high-level replacement systems, new aspects of component modeling and application of graph transformation techniques are discussed:In their contribution on components for algebra transformation systems, Ehrig and Orejas define a component transformation semantics in terms of the semantics of the specifications included in the components. The underlying formal basis of the instantiation of their generic component framework are algebra transformation systems and high-level replacement rules.An application of the formal unifying framework of distributed transformation units is presented by Kuske and Knirsch. The authors illustrate how different features of agent systems can be modeled by distributed graph transformation systems in a uniform way.Another application for graph rewriting, presented by Van Eetvelde and Janssens, is the modeling of refactoring operations for programs. The authors propose a hierarchical graph representation for programs to facilitate the study of refactoring operation effects at class level.The third part contains contributions focusing on unifying concepts for visual modeling techniques including UML:Minas describes a graphical specification tool for DIAGEN, a diagram editor generator based on hypergraph transformation. The specification tool simplifies the specification and generation of diagram editors. It uses an XML-based specification language and comes with a generic XML editor.In his contribution on dynamic aspects of visual modeling languages, Bottoni proposes an approach to the definition of the syntax and semantics of visual languages based on a notion of transition of production/consumption of resources. Abstract meta-models for this notion of transition are presented.An approach to the model-based verification and validation of properties of UML models is presented by Engels, Kïster, Heckel and Lohmann. The authors use graph transformation techniques as a meta-language for the translation and analysis of models.In model-driven architectures, the problem arises to deal with multiple models. Kent and Smith focus in their contribution on bidirectional mappings between models for software requirements and models for software design as basis for tools checking model traceability and consistency.Program CommitteeThe following program committee of UNIGRA'03 has given valuable scientific support: •Hartmut Ehrig (TU Berlin, Germany) [chair]•Roswitha Bardohl (TU Berlin, Germany) [co-chair]•Luciano Baresi (University of Milano, Italy)•Paolo Bottoni (University of Pisa, Italy)•Claudia Ermel (TU Berlin, Germany)•Reiko Heckel (University of Paderborn, Germany)•Dirk Janssens (University of Antwerp, Belgium)•Stuart Kent (University of Kent, Great Britain)•Hans-Jörg Kreowski (University of Bremen, Germany)•Fernando Orejas (University of Catalunya, Espania)•Julia Padberg (University of Bremen, Germany)•Grzegorz Rozenberg (University of Leiden, The Netherlands)AcknowledgementThis workshop is supported by the European research training network SegraVis, and by the steering committee of the International Conference on Graph Transformation (ICGT).June 2003, Roswitha Bardohl and Hartmut Ehrig

Basic Ideas for Transformations of Specification Architectures

This contribution gives the formal foundation for specification architectures. Specification architectures are given by diagrams in an arbitrary category of specifications. Hence this is in line with the extension form graph transformations to high-level replacement systems. We then transform diagrams in order to describe model evolution. We distinguish between global transformations, synchronization, and local transformations. The main result of this paper is that the composition of all sub-specifications, i.e. the semantics of the specification architectures is compatible with the transformation. Hence it guarantees that the result of an architecture transformation is the same as the corresponding transformation of the composed sub-specifications.

A Component Framework Based on High-Level Replacement Systems

This paper is based on two general concepts. The first one is a generic component framework for system modeling presented at FASE 2002, which is especially useful for graph- and net-based modeling techniques. The second one is the concept of high-level replacement systems, which has been studied within the last decade as an abstraction of the DPO-approach for graph transformation systems in a categorical framework, with instantiations to a large class of different modeling techniques. In this contribution both concepts are combined in the sense that the generic transformation concept - essentially used in the component framework - is instantiated by high-level replacement systems. As the main result we show how the properties for transformations required in the component framework can be shown in the case of high-level replacement systems. Moreover, some interesting extensions concerning multiple interfaces, union, and operational semantics of components are proposed.

Basic Results for Two Types of High-Level Replacement Systems

The general idea of high-level replacement systems is to generalize the concept of graph transformation systems and graph grammars from graphs to all kinds of structures which are of interest in Computer Science and Mathematics. Within the algebraic approach of graph transformation this is possible by replacing graphs, graph morphisms, and pushouts (gluing) of graphs by objects, morphisms, and pushouts in a suitable category. Of special interest are categories for all kinds of labelled and typed graphs, hypergraphs, algebraic specifications and Petri nets. In this paper, we review the basic results for high-level replacement systems in the algebraic double-pushout approach in the symmetric case, where both rule morphisms belong to a distinguished class M. Moreover we present for the first time the asymmetric type of high-level replacement systems, where only the left rule morphism K → L belongs to M.

Preface: Volume 44, Issue 4

This volume contains the contributions of the workshop Uniform Approaches to Graphical Process Specification Techniques (UNIGRA'01) held in Genova (31.3. – 1.4.2001) as a satellite of ETAPS 2001. The main idea of this workshop has been to bring together various unifying approaches from the areas of graph transformations, visual modeling techniques and Petri nets due to the increasing amount of divergent formalisms in each of these areas.According to this main idea, this volume presents uniform approaches and further introduces unifying and comparative studies between these fields and related areas.The first part contains contributions from the area of graph transformation with new aspects of GRACE by Kreowski et al. and high-level replacement systems by Parisi-Presicce as unifying approaches to graph transformations and related specification techniques. The main ideas concerning the common exchange formats for graphs and graph transformations discussed within the APPLIGRAPH project and a dynamic meta model for graph transformation approaches are presented in the papers by Taentzer and Heckel, Zündorf respectively. Related work can be found in the handbooks of graph grammars and computing by graph transformation as well as in the proceedings of GRATRA 2000, a satellite of ETAPS 2000.In the second part concerning visual modeling techniques, new aspects of the visual language environments GenGEd and DIAGEN are discussed by Ermel et.al. as well as Minas and Hoffmann respectively. Formal concepts improving different aspects of the UML are studied in three contributions by Groβe-Rhode, Schürr as well as Baresi and Pezze respectively. Related work has been presented at GT-VMT'00, a satellite of ICALP'00 in Geneve and will be presented at GT-VMT'01 as a satellite of ICALP'01 at Heraklion.In the third part, three unifying approaches for Petri nets are proposed by Dehnert et al., Meseguer et al. and by Juhás et al. The first contribution presents the second installment of the “Petri Net Baukasten” developed within the DFG research group “Petri Net Technology”. The first installment has been introduced already at the PNT-Colloquium 1999 in Berlin. A unified presentation of low- and high-level Petri nets is given by Meseguer using their famous unifying framework of rewriting logic. A unified approach for different types of firing rules of Petri nets is given in the paper of Juhás et al. based on partial algebras. A more detailed collection of unifying approaches to Petri Nets is going to appear in a new volume of the series Advances in Petri Net, edited by Ehrig, Juhás, Padberg and Rozenberg.The workshop has stimulated lively discussions between the 35 participants and will certainly lead to further fruitful cooperations.The following program committee of UNIGRA'01 has given valuable scientific support before and during the workshop:Roswitha Bardohl (TU Berlin)Hartmut Ehrig (TU Berlin) [co-chair]Gregor Engels (University of Paderborn)Gabriel Juhas (University of Bratislava/KU Eichstätt)Hans-Järg Kreowski (University of Bremen)Ugo Montanari (University of Pisa)Fernando Orejas (University of Catalunya, Barcelona)Julia Padberg (TU Berlin) [co-chair]Francesco Parisi-Presicce (University La Sapienza, Rome)Grzegorz Rozenberg (University of Leiden)The next UNIGRA workshop is planned as satellite of ETAPS 2003 in Warsaw.This volume will be published as volume 44.4 in the series Electronic Notes in Theoretical Computer Science (ENTCS). This series is published electronically through the facilities of Elsevier Science B.V. and its auspices. The volumes in the ENTCS series can be accessed at the URL http://www.elsevier.nl/locate/entcsThe editors of this volume are most grateful to the organizers of ETAPS'01 and the publisher of ENTCS for their valuable support.Berlin and Genova, May 2001 Hartmut EhrigClaudia ErmelJulia Padberg

On Modifying High Level Replacement Systems

High Level Replacement Systems generalize the concept of graph transformation systems from graphs to other types of structures. Transformation rules to replace a structure with another structure in the same category are defined using morphisms in that category. As with other specification formalisms, replacement systems are subject to modifications during their development process. These modifications could be local changes (individual rules are modified), modular changes (two replacement systems are combined to form a larger system) and global changes (the replacement of a replacement subsystem with another one). These different ways are analyzed and some results are presented to express the behavior of the modified system in terms of the behavior of the original one(s). Applications range from graph transformations to diagrams in visual languages and modelling to algebraic high level nets.

Rule-based refinement of high-level nets preserving safety properties

The concept of rule-based modification developed in the area of algebraic graph transformations and high-level replacement systems has recently shown to be a powerful concept for vertical structuring of Petri nets. This includes low- and high-level Petri nets, especially algebraic high-level nets which can be considered as an integration of algebraic specifications and Petri nets. In a large case study rule-based modification of algebraic high-level nets has been applied successfully for the requirements analysis of a medical information system. The main new result in this paper extends rule-based modification of algebraic high-level nets such that it preserves safety properties formulated in terms of temporal logic. For software development based on rule-based modification of algebraic high-level nets as a vertical development strategy this extension is an important new technique. It is called rule-based refinement. As a running example an important safety property of a medical information system is considered and is shown to be preserved under rule-based refinement.

Categorical Approach to Horizontal Structuring and Refinement of High-Level Replacement Systems

Based on the well-known theory of high-level replacement systems – a categorical formulation of graph grammars – we present new results concerning refinement of high-level replacement systems. Motivated by Petri nets, where refinement is often given by morphisms, we give a categorical notion of refinement. This concept is called Q-transformations and is established within the framework of high-level 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 Q-rules and Q-transformations. Moreover, several concepts and results of high-level replacement systems are extended to Q-transformations. These are sequential and parallel transformations, union, and fusion, based on different colimit constructions. The main results concern the compatibility of these constructions with Q-transformations that is the corresponding theorems for usual transformations are extended to Q-transformations. Finally, we demonstrate the application of these techniques for the special case of Petri nets to a case study concerning the requirements engineering of a medical information system.