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55
Process Bisimulation via a Graphical Encoding
 IN: ICGT ‘06. VOLUME 4178 OF LNCS
, 2006
"... The paper presents a case study on the synthesis of labelled transition systems (ltss) for process calculi, choosing as testbed Milner’s Calculus of Communicating System (ccs). The proposal is based on a graphical encoding: each ccs process is mapped into a graph equipped with suitable interfaces, s ..."
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Cited by 20 (12 self)
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The paper presents a case study on the synthesis of labelled transition systems (ltss) for process calculi, choosing as testbed Milner’s Calculus of Communicating System (ccs). The proposal is based on a graphical encoding: each ccs process is mapped into a graph equipped with suitable interfaces, such that the denotation is fully abstract with respect to the usual structural congruence. Graphs with interfaces are amenable to the synthesis mechanism based on borrowed contexts (bcs), proposed by Ehrig and König (which are an instance of relative pushouts, originally introduced by Milner and Leifer). The bc mechanism allows the effective construction of an lts that has graphs with interfaces as both states and labels, and such that the associated bisimilarity is automatically a congruence. Our paper focuses on the analysis of the lts distilled by exploiting the encoding of ccs processes: besides offering some technical contributions towards the simplification of the bc mechanism, the key result of our work is the proof that the bisimilarity on processes obtained via bcs coincides with the standard strong bisimilarity for ccs.
Rulebased modelling, symmetries, refinements
"... Abstract. Rulebased modelling is particularly effective for handling the highly combinatorial aspects of cellular signalling. The dynamics is described in terms of interactions between partial complexes, and the ability to write rules with such partial complexesi.e., not to have to specify all the ..."
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Abstract. Rulebased modelling is particularly effective for handling the highly combinatorial aspects of cellular signalling. The dynamics is described in terms of interactions between partial complexes, and the ability to write rules with such partial complexesi.e., not to have to specify all the traits of the entitities partaking in a reaction but just those that matter is the key to obtaining compact descriptions of what otherwise could be nearly infinite dimensional dynamical systems. This also makes these descriptions easier to read, write and modify. In the course of modelling a particular signalling system it will often happen that more traits matter in a given interaction than previously thought, and one will need to strengthen the conditions under which that interaction may happen. This is a process that we call rule refinement and which we set out in this paper to study. Specifically we present a method to refine rule sets in a way that preserves the implied stochastic semantics.
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.
Unfoldingbased diagnosis of systems with an evolving topology
, 2008
"... Abstract. We propose a framework for modelbased diagnosis of systems with mobility and variable topologies, modelled as graph transformation systems. Generally speaking, modelbased diagnosis is aimed at constructing explanations of observed faulty behaviours on the basis of a given model of the sy ..."
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Cited by 15 (7 self)
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Abstract. We propose a framework for modelbased diagnosis of systems with mobility and variable topologies, modelled as graph transformation systems. Generally speaking, modelbased diagnosis is aimed at constructing explanations of observed faulty behaviours on the basis of a given model of the system. Since the number of possible explanations may be huge we exploit the unfolding as a compact data structure to store them, along the lines of previous work dealing with Petri net models. Given a model of a system and an observation, the explanations can be constructed by unfolding the model constrained by the observation, and then removing incomplete explanations in a pruning phase. The theory is formalised in a general categorical setting: constraining the system by the observation corresponds to taking a product in the chosen category of graph grammars, so that the correctness of the procedure can be proved by using the fact that the unfolding is a right adjoint and thus it preserves products. The theory thus should be easily applicable to a wide class of system models, including graph grammars and Petri nets. 1
Bisimilarity and BehaviourPreserving Reconfigurations of Open Petri Nets
"... We propose a framework for the specification of behaviourpreserving reconfigurations of systems modelled as Petri nets. The framework is based on open nets, a mild generalisation of ordinary Place/Transition nets suited to model open systems which might interact with the surrounding environment and ..."
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Cited by 12 (5 self)
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We propose a framework for the specification of behaviourpreserving reconfigurations of systems modelled as Petri nets. The framework is based on open nets, a mild generalisation of ordinary Place/Transition nets suited to model open systems which might interact with the surrounding environment and endowed with a colimitbased composition operation. We show that natural notions of (strong and weak) bisimilarity over open nets are congruences with respect to the composition operation. We also provide an upto technique for facilitating bisimilarity proofs. The theory is used to identify suitable classes of reconfiguration rules (in the doublepushout approach to rewriting) whose application preserves the observational semantics of the net.
Composition and decomposition of DPO transformations with borrowed contexts
, 2006
"... Doublepushout (DPO) transformations with borrowed context extend the standard DPO approach by allowing part of the graph needed in a transformation to be borrowed from the environment. The bisimilarity based on the observation of borrowed contexts is a congruence, thus facilitating system analysis ..."
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Cited by 12 (3 self)
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Doublepushout (DPO) transformations with borrowed context extend the standard DPO approach by allowing part of the graph needed in a transformation to be borrowed from the environment. The bisimilarity based on the observation of borrowed contexts is a congruence, thus facilitating system analysis. In this paper, focusing on the situation in which the states of a global system are built out of local components, we show that DPO transformations with borrowed context defined on a global system state can be decomposed into corresponding transformations on the local states and vice versa. Such composition and decomposition theorems, developed in the framework of adhesive categories, can be seen as a first step towards an inductive definition, in sos style, of the labelled transition system associated to a graph transformation system. As a special case we show how an ordinary DPO transformation on a global system state can be decomposed into local DPO transformations with borrowed context using the same production.
Observing reductions in nominal calculi via a graphical encoding of processes
 Processes, terms and cycles (Klop Festschrift), volume 3838 of LNCS
"... Abstract. The paper introduces a novel approach to the synthesis of labelled transition systems for calculi with name mobility. The proposal is based on a graphical encoding: Each process is mapped into a (ranked) graph, such that the denotation is fully abstract with respect to the usual structural ..."
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Cited by 11 (3 self)
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Abstract. The paper introduces a novel approach to the synthesis of labelled transition systems for calculi with name mobility. The proposal is based on a graphical encoding: Each process is mapped into a (ranked) graph, such that the denotation is fully abstract with respect to the usual structural congruence (i.e., two processes are equivalent exactly when the corresponding encodings yield the same graph). Ranked graphs are naturally equipped with a few algebraic operations, and they are proved to form a suitable (bi)category of cospans. Then, as proved by Sassone and Sobocinski, the synthesis mechanism based on relative pushout, originally proposed by Milner and Leifer, can be applied. The resulting labelled transition system has ranked graphs as both states and labels, and it induces on (encodings of) processes an observational equivalence that is reminiscent of early bisimilarity.
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
Toposes are adhesive
 In International Conference on Graph Tranformation, icgt’06, volume 4178 of Lect. Notes Comput. Sc
, 2006
"... Abstract. Adhesive categories have recently been proposed as a categorical foundation for facets of the theory of graph transformation, and have also been used to study techniques from process algebra for reasoning about concurrency. Here we continue our study of adhesive categories by showing that ..."
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Cited by 9 (3 self)
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Abstract. Adhesive categories have recently been proposed as a categorical foundation for facets of the theory of graph transformation, and have also been used to study techniques from process algebra for reasoning about concurrency. Here we continue our study of adhesive categories by showing that toposes are adhesive. The proof relies on exploiting the relationship between adhesive categories, Brown and Janelidze’s work on generalised van Kampen theorems as well as Grothendieck’s theory of descent.
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.