Observational Equivalence for Synchronized Graph Rewriting with Mobility

König, Barbara; Montanari, Ugo

doi:10.1007/3-540-45500-0_7

Cited by 15 publications

(12 citation statements)

References 16 publications

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“…However, there is not yet a uniform theory of bisimulation for graph transformation systems. Previous work on this topic appeared in Baldan et al (2002) and König and Montanari (2001). Adding support, as explained earlier, would be possible in theory, but contradicts the philosophy behind graph rewriting in which graphs are considered only up to isomorphism.…”

Section: Introductionmentioning

confidence: 92%

Deriving bisimulation congruences in the DPO approach to graph rewriting with borrowed contexts

Ehrig¹,

König²

2006

Math. Struct. Comp. Sci.

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Motivated by recent work on the derivation of labelled transitions and bisimulation congruences from unlabelled reaction rules, we show how to address this problem in the DPO (double-pushout) approach to graph rewriting. Unlike the case with previous approaches, we consider graphs as objects, rather than arrows, of the category under consideration. This allows us to present a very simple way of deriving labelled transitions (called rewriting steps with borrowed context), which integrates smoothly with the DPO approach, has a very constructive nature and requires only a minimum of category theory. The core part of this paper is the proof that the bisimilarity based on graph rewriting with borrowed contexts is a congruence relation. We will also introduce some proof techniques and compare our approach with the derivation of labelled transitions via relative pushouts.

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Section: Introductionmentioning

confidence: 92%

Deriving bisimulation congruences in the DPO approach to graph rewriting with borrowed contexts

Ehrig¹,

König²

2006

Math. Struct. Comp. Sci.

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“…Definition 3. 6 We define productions only for standard sequential agents i α i .P i . Let Γ be fn( i α i .P i ).…”

Section: Definition 35 [Translation Of Agents]mentioning

confidence: 99%

“…In this case, the configuration is explicitly represented by a graph which offers both a clean, inherently concurrent mathematical semantics and a suggestive representation. Among the various proposals for graph transformations we choose Synchronized Hyperedge Replacement (SHR) [2,1,6,3]. In our approach we represent computational entities such as processes or hosts with hyperedges (edges connected to an arbitrary number of nodes) and channels between them as shared nodes.…”

Section: Introductionmentioning

confidence: 99%

A Graphical Fusion Calculus

Lanese¹,

Montanari²

2004

Electronic Notes in Theoretical Computer Science

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We analyze the relationship between Fusion Calculus and graph transformations defined in the Synchronized Hyperedge Replacement (SHR) style. In particular we show that the underlying algebraic structure is the same when the synchronization used in SHR is Milner synchronization. The main difference we see is that Fusion Calculus has an interleaving behaviour while SHR is inherently concurrent. In the paper we introduce the interleaving semantics for SHR with Milner synchronization and show that there is a complete correspondence between the operational semantics of Fusion Calculus and of SHR systems.

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“…The Tile Model [41,53,58,19,29,38,8,47,16,42,10,23] combines the modularity of Structured Transition Systems with Meseguer's Rewriting Logic approach. While rewrite rules in Rewriting Logic can be applied in any context and with any actual parameters, the Tile Model allows rewritings to be inhibited under certain contexts.…”

Section: Ugo Montanari's Models Of Computationmentioning

confidence: 99%

Models of Computation: A Tribute to Ugo Montanari’s Vision

Bruni

Sassone

2008

Concurrency, Graphs and Models

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Ugo's research activity in the area of Models of Computation (MoC, for short) has been prominent, influential and broadly scoped. Ugo's trademark is that undefinable ability to understand and distill computational aspects into new models as if you were reading them out of some evident connection between well-know models: only, most often, that connection is really visible only after Ugo shows the way. Like experienced sailors have trusted compasses and sextants to help them find the best routes to harbour, Ugo relies on a bag of favourite tools which he has used along the years to deliver a variety of contributions to the MoC area. To mention just three (in alphabetic order): algebraic techniques, concurrency theory, and unification mechanisms.In this introductory contribution we would like to recall some of the influential MoC models put forward by Ugo which cut across the three approaches. Before doing that, it is worth devoting some space to discuss the three aspects separately. Notably, the use of category theory is a pervasive common trait.Algebraic techniques. By algebraic techniques we refer broadly to the use of universal algebras and initial model semantics; of universal coalgebras and final semantics; and of bialgebras. Many interesting papers witness Ugo's leading role in exploiting algebraic techniques during his entire scientific career. Indeed, his contributions are too many to mention all in the space allocated to this overview; we shall therefore attempt to convey the sense of Ugo's broad-spectrum contribution by recapping only a few key results.Reference [43] is the first paper on final, observational semantics in abstract data types, and the main reference for one of the MoC contributed papers in this volume. It presented several key insights in software specification and development for the first time, like the separation between given sorts and newly specified ones, whereby the given sorts lay the ground to define the observable behaviour for the new sorts. Another key suggestion is that the specification of new data types is often partial -in the sense that it may include "don't care" cases-and that many realisations can exist that exhibit equivalent observable behaviour but are not isomorphic. In fact, [43] shows that the isomorphism classes of observably equivalent algebras conforming to the partial specification form a complete lattice, yielding a so-called loose semantics.Possibly the best known of Ugo's papers, [52] exposes the underlying monoidal structure of the category of Petri net computations. The title itself is revealing: Petri nets are monoids. Besides doing what it says on the tin, this paper opened a long-lasting and fruitful collaboration with José Meseguer, and a research line on the initial semantics of P. Degano et al. (Eds.): Montanari

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Observational Equivalence for Synchronized Graph Rewriting with Mobility

Cited by 15 publications

References 16 publications

Deriving bisimulation congruences in the DPO approach to graph rewriting with borrowed contexts

Deriving bisimulation congruences in the DPO approach to graph rewriting with borrowed contexts

A Graphical Fusion Calculus

Models of Computation: A Tribute to Ugo Montanari’s Vision

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