In order to enable experimentations and simulations of bigraphs, we need an implementation of their dynamic. In this paper, we tackle the matching issue of this task. We present a solution based on an investigation on graph matching. We propose to simulate a bigraphical reactive system (i.e., bigraphs with a set of reaction rules that allow their rewriting) with a graph transformation system. First, we translate a bigraph to a ranked graph. This translation is ensured by defining a faithful functor that allows to move from the bigraph category to the ranked graph category. Then, we show that reaction rules can be simulated with graph rules. Hence, we provide a formal basis allowing to execute bigraph transformations by simulating their translation aiming to use well-established and efficient graph transformation tools.

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In this paper, we present a multi-scale modeling methodology for software System of Systems (SoS) using the formal technique of Bigraphical Reactive System. This methodology provides a correct by design approach ensuring the correctness of the SoS architectures. A first scale is defined by the designer. Then, it is refined by successively adding lower scale details. The transition between scales is implemented following a ruleoriented refinement process. The executed rules respect the system constraints ensuring, in this way, the correctness of the obtained scale architectures. Moreover, we address the dynamic aspect of SoS by providing model-based rules of reconfiguration actions. We illustrate our approach with a Smart Buildings case study.

Abstract. With the evolution of distributed systems in size and complexity, software deployment remains a challenging task. Despite the existence of several approaches, most of them use informal models that lack a solid mathematic foundation. In this paper, we propose a bigraphical based approach for modeling and formalizing the deployment of distributed applications. This approach relies on multi-scale modeling. So, we start by modeling the first scale with a bigraph. This bigraph is enriched, through a series of reaction rules, until reaching the last scale that represents the deployment architecture.

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