Abstract. Bigraphs are emerging as an interesting model for concurrent calculi, like CCS, pi-calculus, and Petri nets. Bigraphs are built orthogonally on two structures: a hierarchical place graph for locations and a link (hyper-)graph for connections. With the aim of describing bigraphical structures, we introduce a general framework for logics whose terms represent arrows in monoidal categories. We then instantiate the framework to bigraphical structures and obtain a logic that is a natural composition of a place graph logic and a link graph logic. We explore the concepts of separation and sharing in these logics and we prove that they generalise some known spatial logics for trees, graphs and tree contexts. 1

Bigraphs have been introduced with the aim to provide a topographical meta-model for mobile, distributed agents that can manipulate their own linkages and nested locations, generalising both characteristics of the π-calculus and the Mobile Ambients calculus. We give the first bigraphical presentation of a non-linear, higher-order process calculus with nested locations, non-linear active process mobility, and local names, the calculus of Higher-Order Mobile Embedded Resources (Homer). The presentation is based on Milner’s recent presentation of the λ-calculus in local bigraphs. The combination of non-linear active process mobility and local names requires a new definition of parametric reaction rules and a representation of the location of names. We suggest localised bigraphs as a generalisation of local bigraphs in which links can be further localised. Key words: bigraphs, local names, non-linear process mobility

Bigraphical Reactive Systems have been proposed as a meta model for global ubiquitous computing generalising process calculi for mobility such as the pi-calculus and the Mobile Ambients calculus as well as graphical models for concurrency such as Petri Nets. We investigate in this paper how Bigraphical Reactive Systems represented as Reactive XML can be used to provide a formal semantics as well as an extensible and mobile platform independent execution format for XML based business process and workflow description languages such as WS-BPEL and XPDL. We propose to extend the formalism with primitives for XPath evaluation and higher-order reaction rules to allow for a very direct and succinct semantics.

Separation Logic and Context Logic have been used to reason locally about heap update and simple tree update. We study local reasoning based on Context Logic for a more realistic, local tree-update language which combines update commands with queries. This combination results in updates at multiple locations, which significantly affects the complexity of the reasoning.

XML-centric models of computation have been proposed as an answer to the demand for interoperability, heterogeneity and openness in coordination models. We present a prototype implementation of an open XML-centric coordination middleware called Distributed Reactive XML. The middleware has as theoretical foundation a general distributed extensible process calculus inspired by the theory of Bigraphical Reactive Systems. The calculus is extensible just as XML is extensible, in that its signature and reaction rules are not fixed. It is distributed by allowing both the state of processesaswellasthesetofreaction rules to be distributed (or partly shared) between different clients. The calculus is implemented by representing process terms as XML documents stored in a value-oriented, peer-to-peer XML Store and reaction rules as XML transformations performed by the clients. The formalism does not require that only process terms are stored—inside process terms one may store application specific data as well. XML Store provides transparent sharing of process terms between all participating peers. Conflicts between concurrent reaction rules are handled by an optimistic concurrency control. The implementation thus provides an open XMLbased coordination middleware with a formal foundation that encompasses both the shared data, processes and reaction rules.

Bigraphs are emerging as a (meta-)model for concurrent calculi, like CCS, ambients, πcalculus, and Petri nets. They are built orthogonally on two structures: a hierarchical place graph for locations and a link (hyper-)graph for connections. Aiming at describing bigraphical structures, we introduce a general framework, BiLog, whose formulae describe arrows in monoidal categories. We then instantiate the framework to bigraphical structures and we obtain a logic that is a natural composition of a place graph logic and a link graph logic. We explore the concepts of separation and sharing in these logics and we prove that they generalise well known spatial logics for trees, graphs and tree contexts. As an application, we show how XML data with links and web services can be modelled by bigraphs and described by BiLog. The framework can be extended by introducing dynamics in the model and a standard temporal modality in the logic. However, in some cases, temporal modalities can be already expressed in the static framework. To testify this, we show how to encode a minimal spatial logic for CCS in an instance of BiLog.

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