Computing (optimal) embeddings of directed bigraphs

Bigraphs and bigraphical reactive systems are a well-known meta-model successfully used for formalizing a wide range of models and situations, such as process calculi, service oriented architectures, multi-agent systems, biological systems, etc. A key problem in the theory and the implementations of bigraphs is how to compute embeddings, i.e., structure-preserving mappings of a given bigraph (the pattern or guest) inside another (the target or host). In this paper, we present an algorithm for computing embeddings for directed bigraphs, an extension of Milner's bigraphs which take into account the request directions between controls and names. This algorithm solves the embedding problem by means of a reduction to a constraint satisfaction problem. We first prove soundness and completeness of this algorithm; then we present an implementation in jLibBig, a general Java library for manipulating bigraphical reactive systems. The effectiveness of this implementation is shown by several experimental results. Finally, we show that this algorithm can be readily adapted to find the optimal embeddings in a weighted variant of the embedding problem

An Algebra for Directed Bigraphs

We study the algebraic structure of directed bigraphs, a bigraphical model of computations with locations, connections and resources previously introduced as a unifying generalization of other variants of bigraphs. We give a sound and complete axiomatization of the (pre)category of directed bigraphs. Using this axiomatization, we give an adequate encoding of the Fusion calculus, showing the utility of the added directnes

DBCChecker: A Bigraph-Based Tool for Checking Security Properties of Container Compositions

Despite their widespread application in modern systems, container composition is often complex and error-prone. In this work, we present DBCChecker, a tool aiming to verify security properties of systems obtained by composition of containers. From the configuration of a container-based system and an abstract description of the interface behaviour of each container, the tool builds a formal model of the overall system, which can be verified in ProVerif (an automatic symbolic protocol verifier), to check that the overall system satisfies the required properties. The system can be described in a specification language capable to express at once the interfaces and connections of containers and the relevant behavioural aspects of their interfaces, called JSON Bigraph Format (JBF), and inspired by previous formal models, based on bigraphs, for containerized architectures

On the Construction of Sorted Reactive Systems

We develop a theory of sorted bigraphical reactive systems. Every application of bigraphs in the literature has required an extension, a sorting, of pure bigraphs. In turn, every such application has required a redevelopment of the theory of pure bigraphical reactive systems for the sorting at hand. Here we present a general construction of sortings. The constructed sortings always sustain the behavioural theory of pure bigraphs (in a precise sense), thus obviating the need to redevelop that theory for each new application. As an example, we recover Milner’s local bigraphs as a sorting on pure bigraphs. Technically, we give our construction for ordinary reactive systems, then lift it to bigraphical reactive systems. As such, we give also a construction of sortings for ordinary reactive systems. This construction is an improvement over previous attempts in that it produces smaller and much more natural sortings, as witnessed by our recovery of local bigraphs as a sorting

Deriving Barbed Bisimulations for Bigraphical Reactive Systems

We study the definition of a general abstract notion of barbed bisimilarity for reactive systems on bigraphs. More precisely, given a bigraphical reactive system, we define the corresponding barbs from the contextual labels given by the IPO construction, in a general and systematic way. These barbs correspond to observe which names on the interface are actually involved in reactions (and how). As examples, we apply this construction to the (bigraphical representation of the) pi-calculus and of Mobile Ambients, and compare the resulting barbed equivalences with those previously known for these calculi

Bigraphical Refinement

We propose a mechanism for the vertical refinement of bigraphical reactive systems, based upon a mechanism for limiting observations and utilising the underlying categorical structure of bigraphs. We present a motivating example to demonstrate that the proposed notion of refinement is sensible with respect to the theory of bigraphical reactive systems; and we propose a sufficient condition for guaranteeing the existence of a safety-preserving vertical refinement. We postulate the existence of a complimentary notion of horizontal refinement for bigraphical agents, and finally we discuss the connection of this work to the general refinement of Reeves and Streader.Comment: In Proceedings Refine 2011, arXiv:1106.348

Graph Algebras for Bigraphs

Binding bigraphs are a graphical formalism intended to be a meta-model for mobile, concurrent and communicating systems. In this paper we present an algebra of typed graph terms which correspond precisely to binding bigraphs over a given signature. As particular cases, pure bigraphs and local bigraphs are described by two sublanguages which can be given a simple syntactic characterization. Moreover, we give a formal connection between these languages and Synchronized Hyperedge Replacement algebras and the hierarchical graphs used in Architectural Design Rewriting. This allows to transfer results and constructions among formalisms which have been developed independently, e.g., the systematic definition of congruent bisimulations for SHR graphs via the IPO construction

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

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