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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 ..."
Abstract

Cited by 996 (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 ..."
Abstract

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 ..."
Abstract

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
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
Transition systems, link graphs and Petri nets
, 2004
"... A framework is defined within which reactive systems can be studied formally. The framework is based upon scategories, a new variety of categories, within which reactive systems can be set up in such a way that labelled transition systems can be uniformly extracted. These lead in turn to behavi ..."
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Cited by 26 (5 self)
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A framework is defined within which reactive systems can be studied formally. The framework is based upon scategories, a new variety of categories, within which reactive systems can be set up in such a way that labelled transition systems can be uniformly extracted. These lead in turn to behavioural preorders and equivalences, such as the failures preorder (treated elsewhere) and bisimilarity, which are guaranteed to be congruential. The theory rests upon the notion of relative pushout previously introduced by the authors. The framework