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92
Bigraphs and Mobile Processes
, 2003
"... A bigraphical reactive system (BRS) involves bigraphs, in which the nesting of nodes represents locality, independently of the edges connecting them; it also allows bigraphs to reconfigure themselves. BRSs aim to provide a uniform way to model spatially distributed systems that both compute and comm ..."
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Cited by 995 (29 self)
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A bigraphical reactive system (BRS) involves bigraphs, in which the nesting of nodes represents locality, independently of the edges connecting them; it also allows bigraphs to reconfigure themselves. BRSs aim to provide a uniform way to model spatially distributed systems that both compute and communicate. In this memorandum we develop their static and dynamic theory. In part I, we illustrate...
Deriving Bisimulation Congruences in the DPO Approach to Graph Rewriting
, 2004
"... Motivated by recent work on the derivation of labelled transitions and bisimulation congruences from unlabelled reaction rules, we show how to solve this problem in the DPO (doublepushout) approach to graph rewriting. Unlike in previous approaches, we consider graphs as objects, instead of arrows, ..."
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Cited by 62 (11 self)
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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 solve this problem in the DPO (doublepushout) approach to graph rewriting. Unlike in previous approaches, we consider graphs as objects, instead of 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 smoothly integrates 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 sketch that the bisimilarity based on rewriting with borrowed contexts is a congruence relation.
Bigraphs and Mobile Processes (revised)
, 2004
"... A bigraphical reactive system (BRS) involves bigraphs, in which the nesting of nodes represents locality, independently of the edges connecting them; it also allows bigraphs to reconfigure themselves. BRSs aim to provide a uniform way to model spatially distributed systems that both compute and comm ..."
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Cited by 59 (6 self)
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A bigraphical reactive system (BRS) involves bigraphs, in which the nesting of nodes represents locality, independently of the edges connecting them; it also allows bigraphs to reconfigure themselves. BRSs aim to provide a uniform way to model spatially distributed systems that both compute and communicate. In this memorandum we develop their static and dynamic theory. In Part I we illustrate...
Pure bigraphs: structure and dynamics
, 2005
"... Bigraphs are graphs whose nodes may be nested, representing locality, independently of the edges connecting them. They may be equipped with reaction rules, forming a bigraphical reactive system (Brs) in which bigraphs can reconfigure themselves. Following an earlier paper describing link graphs, a c ..."
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Cited by 51 (5 self)
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Bigraphs are graphs whose nodes may be nested, representing locality, independently of the edges connecting them. They may be equipped with reaction rules, forming a bigraphical reactive system (Brs) in which bigraphs can reconfigure themselves. Following an earlier paper describing link graphs, a constituent of bigraphs, this paper is a devoted to pure bigraphs, which in turn underlie various more refined forms. Elsewhere it is shown that behavioural analysis for Petri nets, πcalculus and mobile ambients can all be recovered in the uniform framework of bigraphs. The paper first develops the dynamic theory of an abstract structure, a wide reactive system (Wrs), of which a Brs is an instance. In this context, labelled transitions are defined in such a way that the induced bisimilarity is a congruence. This work is then specialised to Brss, whose graphical structure allows many refinements of the theory. The latter part of the paper emphasizes bigraphical theory that is relevant to the treatment of dynamics via labelled transitions. As a running example, the theory is applied to finite pure CCS, whose resulting transition system and bisimilarity are analysed in detail. The paper also mentions briefly the use of bigraphs to model pervasive computing and
A calculus of mobile resources
, 2002
"... We introduce a calculus of Mobile Resources (MR) tailored for the design and analysis of systems containing mobile, possibly nested, computing devices that may have resource and access constraints, and which are not copyable nor modifiable per se. We provide a reduction as well as a labelled tran ..."
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Cited by 39 (11 self)
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We introduce a calculus of Mobile Resources (MR) tailored for the design and analysis of systems containing mobile, possibly nested, computing devices that may have resource and access constraints, and which are not copyable nor modifiable per se. We provide a reduction as well as a labelled transition semantics and prove a correspondence between barbed bisimulation congruence and a higherorder bisimulation. We provide examples of the expressiveness of the calculus, and apply the theory to prove one of its characteristic properties. This report is the full version of [11].
Axioms For Bigraphical Structure
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2005
"... This paper axiomatises the structure of bigraphs, and proves that the resulting theory is complete. Bigraphs are graphs with double structure, representing locality and connectivity. They have been shown to represent dynamic theories for the #calculus, mobile ambients and Petri nets, in a way th ..."
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Cited by 36 (8 self)
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This paper axiomatises the structure of bigraphs, and proves that the resulting theory is complete. Bigraphs are graphs with double structure, representing locality and connectivity. They have been shown to represent dynamic theories for the #calculus, mobile ambients and Petri nets, in a way that is faithful to each of those models of discrete behaviour. While the main purpose of bigraphs is to understand mobile systems, a prerequisite for this understanding is a wellbehaved theory of the structure of states in such systems. The algebra of bigraph structure is surprisingly simple, as the paper demonstrates; this is because bigraphs treat locality and connectivity orthogonally
Reactive Systems over Cospans
, 2005
"... The theory of reactive systems, introduced by Leifer and Milner and previously extended by the authors, allows the derivation of wellbehaved labelled transition systems (LTS) for semantic models with an underlying reduction semantics. The derivation procedure requires the presence of certain colimi ..."
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Cited by 36 (2 self)
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The theory of reactive systems, introduced by Leifer and Milner and previously extended by the authors, allows the derivation of wellbehaved labelled transition systems (LTS) for semantic models with an underlying reduction semantics. The derivation procedure requires the presence of certain colimits (or, more usually and generally, bicolimits) which need to be constructed separately within each model. In this paper, we o#er a general construction of such bicolimits in a class of bicategories of cospans. The construction sheds light on as well as extends Ehrig and Konig's rewriting via borrowed contexts and opens the way to a unified treatment of several applications.
Operational congruences for reactive systems
, 2001
"... This document consists of a slightly revised and corrected version of a dissertation ..."
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Cited by 34 (4 self)
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This document consists of a slightly revised and corrected version of a dissertation
Bigraphs for Petri nets
, 2004
"... A simple example is given of the use of bigraphical reactive systems (BRSs). It provides a behavioural semantics for conditionevent Petri nets whose interfaces are named condition nodes, using a simple form of BRS equipped with a labelled transition system and its associated bisimilarity equivalenc ..."
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Cited by 33 (3 self)
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A simple example is given of the use of bigraphical reactive systems (BRSs). It provides a behavioural semantics for conditionevent Petri nets whose interfaces are named condition nodes, using a simple form of BRS equipped with a labelled transition system and its associated bisimilarity equivalence. Both of the latter are derived from the standard net firing rules by a uniform technique in bigraphs, which also ensures that the bisimilarity is a congruence. Furthermore, this bisimilarity is shown to coincide with one induced by a natural notion of experiment on conditionevent nets, defined independently of bigraphs. The paper
Saturated semantics for reactive systems
 LOGIC IN COMPUTER SCIENCE
, 2006
"... The semantics of process calculi has traditionally been specified by labelled transition systems (LTS), but with the development of name calculi it turned out that reaction rules (i.e., unlabelled transition rules) are often more natural. This leads to the question of how behavioural equivalences (b ..."
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Cited by 28 (17 self)
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The semantics of process calculi has traditionally been specified by labelled transition systems (LTS), but with the development of name calculi it turned out that reaction rules (i.e., unlabelled transition rules) are often more natural. This leads to the question of how behavioural equivalences (bisimilarity, trace equivalence, etc.) defined for LTS can be transferred to unlabelled transition systems. Recently, in order to answer this question, several proposals have been made with the aim of automatically deriving an LTS from reaction rules in such a way that the resulting equivalences are congruences. Furthermore these equivalences should agree with the intended semantics, whenever one exists. In this paper we propose saturated semantics, based on a weaker notion of observation and orthogonal to all the previous proposals, and we demonstrate the appropriateness of our semantics by means of two examples: logic programming and a subset of the open πcalculus. Indeed, we prove that our equivalences are congruences and that they coincide with logical equivalence and open bisimilarity respectively, while equivalences studied in previous works are strictly finer.