Spatial Logics for Bigraphs

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

Variable binding, symmetric monoidal closed theories, and bigraphs

This paper investigates the use of symmetric monoidal closed (SMC) structure for representing syntax with variable binding, in particular for languages with linear aspects. In our setting, one first specifies an SMC theory T, which may express binding operations, in a way reminiscent from higher-order abstract syntax. This theory generates an SMC category S(T) whose morphisms are, in a sense, terms in the desired syntax. We apply our approach to Jensen and Milner's (abstract binding) bigraphs, which are linear w.r.t. processes. This leads to an alternative category of bigraphs, which we compare to the original.Comment: An introduction to two more technical previous preprints. Accepted at Concur '0

Towards a bigraphical encoding of actors

Actors are self-contained, concurrently interacting entities of a computing system. They can perform local computations, communicate via asynchronous message passing with other actors and can be dynamically created. Bigraphs are a fully graphical process algebraic formalism, capable of representing both the position in space of agents and their inter-connections. Their behaviour is specified by a set of reaction rules. In this paper, we present a bigraphical encoding of a simplified actor language with static topology. We express actor configurations in terms of sorted bigraphs while the rules of the actor operational semantics are encoded by bigraphical reactive rules

Bigraphical Logics for XML

Bigraphs have been recently proposed as a meta-model for global computing resources; they are built orthogonally on two structures: a hierarchical ‘place’ graph for locations and a ‘link’ (hyper-)graph for connections. XML is now the standard meta-language for the data exchange and storage on the web. In this paper we address the similarities between bigraphs and XML and we propose bigraphs as a rich model for XML (and XML contexts). Building on this idea we proceed by investigating how the recently proposed logic of BiLog can be instantiated to describe, query and reason about web data (and web contexts)

Towards a bigraphical encoding of actors

Actors are self-contained, concurrently interacting entities of a computing system. They can perform local computations, communicate via asynchronous message passing with other actors and can be dynamically created. Bigraphs are a fully graphical process algebraic formalism, capable of representing both the position in space of agents and their inter-connections. Their behaviour is specified by a set of reaction rules. In this paper, we present a bigraphical encoding of a simplified actor language with static topology. We express actor configurations in terms of sorted bigraphs while the rules of the actor operational semantics are encoded by bigraphical reactive rules

Controlling resource access in Directed Bigraphs

We study directed bigraph with negative ports, a bigraphical framework for representing models for distributed, concurrent and ubiquitous computing. With respect to previous versions, we add the possibility that components may govern the access to resources, like (web) servers control requests from clients. This framework encompasses many common computational aspects, such as name or channel creation, references, client/server connections, localities, etc, still allowing to derive systematically labelled transition systems whose bisimilarities are congruences. As application examples, we analyse the encodings of client/server communications through firewalls, of (compositional) Petri nets and of chemical reactions

Binding bigraphs as symmetric monoidal closed theories

Milner's bigraphs are a general framework for reasoning about distributed and concurrent programming languages. Notably, it has been designed to encompass both the pi-calculus and the Ambient calculus. This paper is only concerned with bigraphical syntax: given what we here call a bigraphical signature K, Milner constructs a (pre-) category of bigraphs BBig(K), whose main features are (1) the presence of relative pushouts (RPOs), which makes them well-behaved w.r.t. bisimulations, and that (2) the so-called structural equations become equalities. Examples of the latter include, e.g., in pi and Ambient, renaming of bound variables, associativity and commutativity of parallel composition, or scope extrusion for restricted names. Also, bigraphs follow a scoping discipline ensuring that, roughly, bound variables never escape their scope. Here, we reconstruct bigraphs using a standard categorical tool: symmetric monoidal closed (SMC) theories. Our theory enforces the same scoping discipline as bigraphs, as a direct property of SMC structure. Furthermore, it elucidates the slightly mysterious status of so-called links in bigraphs. Finally, our category is also considerably larger than the category of bigraphs, notably encompassing in the same framework terms and a flexible form of higher-order contexts.Comment: 17 pages, uses Paul Taylor's diagram

Reactive Systems over Cospans

The theory of reactive systems, introduced by Leifer and Milner and previously extended by the authors, allows the derivation of well-behaved 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 offer 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

A Bigraphical Vending Machine as a Webservice: From Specification and Analysis to Implementation using the Bigraph Toolkit Suite

A bigraph-driven vending machine is implemented. The application is realized as a Spring-based webservice. Actions can be initiated by REST endpoints. The system follows a rule-based architecture, where possible operations are grounded on a rule set. Bigraphical Reactive Systems are used for the specification and execution. The actual state of the application is a bigraph stored in a database, which can be viewed and altered directly in the database. A history of states is kept - the application can be transferred to any prior state. The application can be updated or extended by merely changing the bigraphical database model.:First Part: A system of a vending machine is specified and analyzed using BDSL. This concerns the static and dynamic aspects of the system. Second Part: The analysis results are re-used for the implementation using Bigraph Framework. The application is realized as a webservice that is built using the Spring framework.Ein bigraph-gesteuerter Verkaufsautomat wird implementiert. Die Anwendung ist als Spring-basierter Webservice realisiert. Aktionen können über REST-Endpunkte initiiert werden. Das System folgt einer regelbasierten Architektur, bei der die möglichen Operationen auf einem Regelsatz beruhen. Für die Spezifikation und Ausführung werden Bigraphical Reactive Systems verwendet. Der aktuelle Zustand der Anwendung ist ein in einer Datenbank gespeicherter Bigraph, der direkt in der Datenbank eingesehen und verändert werden kann. Es wird eine Historie der Zustände geführt - die Anwendung kann in einen beliebigen früheren Zustand überführt werden. Die Anwendung kann aktualisiert oder erweitert werden, indem lediglich das bigraphische Datenbankmodell geändert wird.:First Part: A system of a vending machine is specified and analyzed using BDSL. This concerns the static and dynamic aspects of the system. Second Part: The analysis results are re-used for the implementation using Bigraph Framework. The application is realized as a webservice that is built using the Spring framework