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Contextual petri nets, asymmetric event structures and processes
 Information and Computation
, 2001
"... We present an event structure semantics for contextual nets, an extension of P/T Petri nets where transitions can check for the presence of tokens without consuming them (readonly operations). A basic rôle is played by asymmetric event structures, a generalization of Winskel’s prime event structure ..."
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Cited by 43 (14 self)
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We present an event structure semantics for contextual nets, an extension of P/T Petri nets where transitions can check for the presence of tokens without consuming them (readonly operations). A basic rôle is played by asymmetric event structures, a generalization of Winskel’s prime event structures where symmetric conflict is replaced by a relation modelling asymmetric conflict or weak causality, used to represent a new kind of dependency between events arising in contextual nets. Extending Winskel’s seminal work on safe nets, the truly concurrent event based semantics of contextual nets is given at categorical level via a chain of coreflections
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 24 (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.
Processes for adhesive rewriting systems
 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2006
"... Rewriting systems over adhesive categories have been recently introduced as a general framework which encompasses several rewritingbased computational formalisms, including various modelling frameworks for concurrent and distributed systems. Here we begin the development of a truly concurrent seman ..."
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Cited by 16 (11 self)
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Rewriting systems over adhesive categories have been recently introduced as a general framework which encompasses several rewritingbased computational formalisms, including various modelling frameworks for concurrent and distributed systems. Here we begin the development of a truly concurrent semantics for adhesive rewriting systems by defining the fundamental notion of process, wellknown from Petri nets and graph grammars. The main result of the paper shows that processes capture the notion of true concurrency—there is a onetoone correspondence between concurrent derivations, where the sequential order of independent steps is immaterial, and (isomorphism classes of) processes. We see this contribution as a step towards a general theory of true concurrency which specialises to the various concrete constructions found in the literature.
Static Analysis of Distributed Systems with Mobility Specified by Graph Grammars  A Case Study
 PROC. OF IDPT ’02 (SIXTH INTERNATIONAL CONFERENCE ON INTEGRATED DESIGN & PROCESS TECHNOLOGY). SOCIETY FOR DESIGN AND PROCESS SCIENCE
, 2002
"... We consider a distributed system with mobility modelled as a graph transformation system. Then we show that nonsecure level processes cannot influence secure level processes, a property formalized as the absence of causal dependencies between such processes. This is done by resorting to an analysis ..."
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Cited by 10 (7 self)
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We consider a distributed system with mobility modelled as a graph transformation system. Then we show that nonsecure level processes cannot influence secure level processes, a property formalized as the absence of causal dependencies between such processes. This is done by resorting to an analysis technique for graph transformation systems, called approximated unfolding, based on the construction of an approximation of the unfolding semantics.
Unfolding Semantics of Graph Transformation
, 2007
"... Several attempts have been made of extending to graph grammars the unfolding semantics originally developed by Winskel for (safe) Petri nets, but only partial results were obtained. In this paper we fully extend Winskel’s approach to singlepushout grammars providing them with a categorical concurre ..."
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Cited by 10 (8 self)
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Several attempts have been made of extending to graph grammars the unfolding semantics originally developed by Winskel for (safe) Petri nets, but only partial results were obtained. In this paper we fully extend Winskel’s approach to singlepushout grammars providing them with a categorical concurrent semantics expressed as a
Unfolding of doublepushout graph grammars is a coreflection
 PROCEEDINGS INTERNATIONAL WORKSHOP ON THEORY AND APPLICATION OF GRAPH TRANSFORMATIONS, VOLUME 1764 OF LECT. NOTES IN COMP. SCI
, 1999
"... In a recent paper, mimicking Winskel’s construction for Petri nets, a concurrent semantics for (doublepushout) DPO graph grammars has been provided by showing that each graph grammar can be unfolded into an acyclic branching structure, that is itself a (nondeterministic occurrence) graph grammar d ..."
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Cited by 9 (7 self)
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In a recent paper, mimicking Winskel’s construction for Petri nets, a concurrent semantics for (doublepushout) DPO graph grammars has been provided by showing that each graph grammar can be unfolded into an acyclic branching structure, that is itself a (nondeterministic occurrence) graph grammar describing all the possible computations of the original grammar. This paper faces the problem of providing a closer correspondence with Winskel’s result by showing that the unfolding construction can be described
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 9 (7 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.
Concurrency and Nondeterminism in Graph Rewriting: From Graph Grammars to Asymmetric Event Structures and Backwards
, 2005
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Cited by 2 (2 self)
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