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Confluence of Typed Attributed Graph Transformation Systems
 In: Proc. ICGT 2002. Volume 2505 of LNCS
, 2002
"... The issue of confluence is of major importance for the successful application of attributed graph transformation, such as automated translation of UML models into semantic domains. Whereas termination is undecidable in general and must be established by carefully designing the rules, local confl ..."
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Cited by 53 (10 self)
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The issue of confluence is of major importance for the successful application of attributed graph transformation, such as automated translation of UML models into semantic domains. Whereas termination is undecidable in general and must be established by carefully designing the rules, local confluence can be shown for term rewriting and graph rewriting using the concept of critical pairs. In this paper, we discuss typed attributed graph transformation using a new simplified notion of attribution. For this kind of attributed graph transformation systems we establish a definition of critical pairs and prove a critical pair lemma, stating that local confluence follows from confluence of all critical pairs.
Concurrent semantics of algebraic graph transformation
 Handbook of Graph Grammars and Computing by Graph Transformation
, 1999
"... Graph transformation systems are widely recognized as a powerful formalism for the specification of concurrent and distributed systems. Therefore, the need emerges naturally of developing formal concurrent semantics for graph transformation systems allowing for a suitable description and analysis of ..."
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Cited by 23 (4 self)
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Graph transformation systems are widely recognized as a powerful formalism for the specification of concurrent and distributed systems. Therefore, the need emerges naturally of developing formal concurrent semantics for graph transformation systems allowing for a suitable description and analysis of their computational properties. The aim of this chapter is to review and compare various concurrent semantics for the double pushout (DPO) algebraic approach to graph transformation, using different mathematical structures and describing computations at different levels of abstraction. We first present a trace semantics, based on the classical shift equivalence on graph derivations. Next we introduce graph processes, which lift to the graph transformation framework the notion of nonsequential process for Petri nets. Trace and process semantics are shown to be equivalent, in the sense that given a graph transformation system, the corresponding category of derivation traces and that of (concatenable) processes turns out to be isomorphic. Finally, a more abstract description of graph transformation systems computations is given by defining a semantics based on Winskel’s event structures.
Concatenable graph processes: relating processes and derivation traces
 IN PROCEEDINGS OF ICALP’98, VOLUME 1443 OF LNCS
, 1998
"... Several formal concurrent semantics have been proposed for graph rewriting, a powerful formalism for the specification of concurrent and distributed systems which generalizes P/T Petri nets. In this paper we relate two such semantics recently proposed for the algebraic doublepushout approach to gra ..."
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Cited by 19 (14 self)
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Several formal concurrent semantics have been proposed for graph rewriting, a powerful formalism for the specification of concurrent and distributed systems which generalizes P/T Petri nets. In this paper we relate two such semantics recently proposed for the algebraic doublepushout approach to graph rewriting, namely the derivation trace and the graph process semantics. The notion of concatenable graph process is
A BiCategorical Axiomatisation of Concurrent Graph Rewriting
, 1999
"... In this paper the concurrent semantics of doublepushout (DPO) graph rewriting, which is classically defined in terms of shiftequivalence classes of graph derivations, is axiomatised via the construction of a free monoidal bicategory. In contrast to a previous attempt based on 2categories, the us ..."
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Cited by 18 (10 self)
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In this paper the concurrent semantics of doublepushout (DPO) graph rewriting, which is classically defined in terms of shiftequivalence classes of graph derivations, is axiomatised via the construction of a free monoidal bicategory. In contrast to a previous attempt based on 2categories, the use of bicategories allows to define rewriting on concrete graphs. Thus, the problem of composition of isomorphism classes of rewriting sequences is avoided. Moreover, as a first step towards the recovery of the full expressive power of the formalism via a purely algebraic description, the concept of disconnected rules is introduced, i.e., rules whose interface graphs are made of disconnected nodes and edges only. It is proved that, under reasonable assumptions, rewriting via disconnected rules enjoys similar concurrency properties like in the classical approach.
Concurrent Computing: from Petri Nets to Graph Grammars
 Electronic Notes in Theoretical Computer Science
, 1995
"... Petri nets are widely accepted as a specification formalism for concurrent and distributed systems. One of the reasons of their success is the fact that they are equipped with a rich theory, including wellunderstood concurrent semantics; they also provide an interesting benchmark for tools and tech ..."
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Cited by 9 (0 self)
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Petri nets are widely accepted as a specification formalism for concurrent and distributed systems. One of the reasons of their success is the fact that they are equipped with a rich theory, including wellunderstood concurrent semantics; they also provide an interesting benchmark for tools and techniques for the description of concurrent systems. Graph grammars can be regarded as a proper generalization of Petri nets, where the current state of a system is described by a graph instead as by a collection of tokens. In this tutorial paper I will review some basic definitions and constructions concerning the concurrent semantics of nets, and I will show to what extent corresponding notions have been developed for graph grammars. Most of such results come out from a joint research by the Berlin and Pisa COMPUGRAPH groups. 1 Introduction The nets which owe their name to Carl Adam Petri [28,29] have been the first formal tool proposed for the specification of the behaviour of systems which...
Subobject Transformation Systems
, 2008
"... Subobject transformation systems (STS) are proposed as a novel formal framework for the analysis of derivations of transformation systems based on the algebraic, doublepushout (DPO) approach. They can be considered as a simplified variant of DPO rewriting, acting in the distributive lattice of subo ..."
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Cited by 6 (4 self)
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Subobject transformation systems (STS) are proposed as a novel formal framework for the analysis of derivations of transformation systems based on the algebraic, doublepushout (DPO) approach. They can be considered as a simplified variant of DPO rewriting, acting in the distributive lattice of subobjects of a given object of an adhesive category. This setting allows a direct analysis of all possible notions of dependency between any two productions without requiring an explicit match. In particular, several equivalent characterizations of independence of productions are proposed, as well as a local Church–Rosser theorem in the setting of STS. Finally, we show how any derivation tree in an ordinary DPO grammar leads to an STS via a suitable construction and show that relational reasoning in the resulting STS is sound and complete with respect to the independence in the original derivation tree.
Term Rewriting with Sharing and Memoïzation
 Algebraic and Logic Programming: Proc. of the Third International Conference
, 1992
"... Jungle evaluation is an approach to define term rewriting with sharing based on graph grammars. This approach preserves important properties of term rewriting like termination, and confluence for terminating systems (under mild restrictions). In this paper, term rewriting with sharing is further acc ..."
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Cited by 3 (1 self)
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Jungle evaluation is an approach to define term rewriting with sharing based on graph grammars. This approach preserves important properties of term rewriting like termination, and confluence for terminating systems (under mild restrictions). In this paper, term rewriting with sharing is further accelerated, by memoization known from functional programming languages: The result of evaluating a function with some arguments is tabulated so that it can be looked up later on when the function is reapplied to the same arguments. We show that term rewriting with sharing and memoization is correct and complete w.r.t. jungle evaluation if the rules are nonoverlapping and nonlooping. Redundant reevaluation of functions is avoided, independent of a particular strategy for applying evaluation rules. 1 Introduction Term rewriting is a basis for prototyping algebraic specifications of abstract data types, and a foundation of functional programming languages (see [DJ90] and [Klo90] for overvie...
Towards a Notion of Transaction in Graph Rewriting
, 2006
"... We define transactional graph transformation systems (tgtss), a mild extension of the ordinary framework for the doublepushout approach to graph transformation, which allows to model transactional activities. Generalising the work on zerosafe nets, the new graphical formalism is based on a typing ..."
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Cited by 1 (1 self)
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We define transactional graph transformation systems (tgtss), a mild extension of the ordinary framework for the doublepushout approach to graph transformation, which allows to model transactional activities. Generalising the work on zerosafe nets, the new graphical formalism is based on a typing discipline which induces a distinction between stable and unstable items. A transaction is then a suitably defined minimal computation which starts and ends in stable states. After providing the basics of tgtss, we illustrate the expected results, needed to bring the theory to full maturity, and some possible future developments.
Shifting Derivations of noninjective Rules in the Algebraic Graph Rewriting Approaches
, 1997
"... In the algebraic graph rewriting approaches many results are achieved in the field of true concurrency for injective rules only. Especially the SHIFT operator, which allows the interchanging of two consecutive rule applications if these are sequentially independent, is of interest in analysis of der ..."
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In the algebraic graph rewriting approaches many results are achieved in the field of true concurrency for injective rules only. Especially the SHIFT operator, which allows the interchanging of two consecutive rule applications if these are sequentially independent, is of interest in analysis of derivation sequences. The SHIFT operator allows to shift rule applications from some position in a derivation sequence to another, if it results in an equal derivation sequence. But the shifting of rule applications should preserve the sequential independence and dependence of subsequences. In the general case of noninjective rules and noninjective matches the SHIFT operator does not preserve this properties in all situations. The behavior of the SHIFT operator is fully examined and restrictions for the rule applications are given to ensure the preserving of sequentially independence and dependence in any situation. Introduction In the algebraic graph rewriting approaches, SinglePushout and...
Concurrency for Graph Grammars in a Petri net shell
, 2011
"... Graph grammars are a powerful model of concurrent and distributed systems which can be seen as a proper extension of Petri nets. Inspired by this correspondence we develop truly concurrent semantics for dpo graph grammars based on (deterministic) processes and on a Winskel’s style unfolding construc ..."
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Graph grammars are a powerful model of concurrent and distributed systems which can be seen as a proper extension of Petri nets. Inspired by this correspondence we develop truly concurrent semantics for dpo graph grammars based on (deterministic) processes and on a Winskel’s style unfolding construction, and we show that the two approaches can be reconciled. A basic role is played by the study of contextual and inhibitor nets, two extensions of ordinary nets which can be seen as intermediate models between graph grammars and ordinary Petri nets.