Bigraphical Reactive Systems Research Articles

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. • We introduce an algorithm for computing embeddings of directed bigraphs. • We prove the soundness and completeness of the algorithm. • We implement the algorithm and perform an empirical evaluation of the algorithm. • We adapt the algorithm to compute optimal embeddings in a weighted variant of the embedding problem.

A Fault Tolerance and Recovery Formal Model for IoT Systems

In an increasingly connected world, the internet of Things (IoT), Cloud and Fog computing are a major asset allowing to overcome previously inconceivable limits in terms of innovation. However, Fault Tolerance remains a major challenge for assuring IoT systems dependability. In order to tackle this issue, we propose a generic microservice architecture called FaTMA (Fault Tolerance- Microservice Architecture for IoT) permitting detection of Things failures by providing continuous and real-time monitoring of their states. In addition, it offers mechanisms to strengthen the reliability of the designed systems. We adopt Bigraphical Reactive Systems (BRS) as formalism to define a formal model that describes architectural elements of different IoT system layers and their behavior. It provides a clear separation between the various microservices controlling this system type and their side effects. Indeed, the execution of the proposed model, through BigraphER tool, permits to simulate and analyze different failure scenarios as well as their restitution strategies.

Design and Verification of Multi-Agent Systems with the Use of Bigraphs

Widespread access to low-cost, high computing power allows for increased computerization of everyday life. However, high-performance computers alone cannot meet the demands of systems such as the Internet of Things or multi-agent robotic systems. For this reason, modern design methods are needed to develop new and extend existing projects. Because of high interest in this subject, many methodologies for designing the aforementioned systems have been developed. None of them, however, can be considered the default one to which others are compared to. Any useful methodology must provide some tools, versatility, and capability to verify its results. This paper presents an algorithm for verifying the correctness of multi-agent systems modeled as tracking bigraphical reactive systems and checking whether a behavior policy for the agents meets non-functional requirements. Memory complexity of methods used to construct behavior policies is also discussed, and a few ways to reduce it are proposed. Detailed examples of algorithm usage have been presented involving non-functional requirements regarding time and safety of behavior policy execution.

A tale of two graph models: a case study in wireless sensor networks

Designing and reasoning about complex systems such as wireless sensor networks is hard due to highly dynamic environments: sensors are heterogeneous, battery-powered, and mobile. While formal modelling can provide rigorous mechanisms for design/reasoning, they are often viewed as difficult to use. Graph rewrite-based \tmodelling techniques increase usability by providing an intuitive, flexible, and diagrammatic form of modelling in which graph-like structures express relationships between entities while rewriting mechanisms allow model evolution. Two major graph-based formalisms are Graph Transformation Systems (GTS) and Bigraphical Reactive Systems (BRS). While both use similar underlying structures, how they are employed in modelling is quite different. To gain a deeper understanding of GTS and BRS, and to guide future modelling, theory, and tool development, in this experience report we compare the practical modelling abilities and style of GTS and BRS when applied to topology control in WSNs. To show the value of the models, we describe how analysis may be performed in both formalisms. A comparison of the approaches shows that although the two formalisms are different, from both a theoretical and practical modelling standpoint, they are each successful in modelling topology control in WSNs. We found that GTS, while featuring a small set of entities and transformation rules, relied on entity attributes, rule application based on attribute/variable side-conditions, and imperative control flow units. BRS on the other hand, required a larger number of entities in order to both encode attributes directly in the model (via nesting) and provide tagging functionality that, when coupled with rule priorities, implements control flow. There remains promising research mapping techniques between the formalisms to further enable flexible and expressive modelling.

A multi-layered bigraphical modelling approach for context-aware systems

There exist several approaches proposed for building Context-Aware Systems (CAS). However, due to the continually changing environment, the large number of interrelated components, complexity and diversity of application domains make the modelling of context-aware systems a particularly challenging task. To address the increasing complexity of the modelling: i) It is critical to take into account the importance of the environment (operational context); and ii) rely on software engineering concepts such as abstraction and modularity in order to reduce the level of complexity. Also, a context-aware system may require intelligence and autonomy. These naturally lead us to apply intelligent agent-based engineering. This work introduces a formal layered design approach that combines intelligent control of multi-agent systems and bigraph's rigor to model context-aware systems. Bigraphical reactive systems are particularly compelling for their capacity to specify, simultaneously, the physical and logical distribution of system components and their interconnections using two distinct structures; that is: place graph and link graph. While the behaviour and dynamic evolution are expressed using defined reaction rules, and as a last step, the bigraph specifications are coded in the Maude language to allow their execution and the verification of their validity.

BigNFC: Novel Formal model for NFC based context-aware applications

Context-aware computing refers to system ability to sense its environment and modify its behavior for delivering suitable services. Having such kind of systems with the Near Field Communication (NFC) capability, opens new perspectives and research areas, allowing very useful type of applications known as NFC-based context-aware applications. These systems require correctness due to their applicability and then need to be proven formally using exhaustive analysis approach such as formal verification. In literature, most of works focuses on creating a general model for context aware systems ignoring the specificity of certain applications such as NFC applications where they present a higher complexity. We emphasize the existence of little or no work in this area supporting formal modeling. To boost it, we propose BigNFC as a novel formal-model based on Bigraphical Reactive Systems (BRS) taking account the interaction mode from the beginning, so we establish mapping between BRS and BigNFC components, where the structures are modelled as bigraphs and behaviors as rewriting rules. Finally, to validate our model, we have applied it on a real-life application and some properties were checked successfully.

SLA-Driven modeling and verifying cloud systems: A Bigraphical reactive systems-based approach

We propose a formal approach based on Bigraphical Reactive Systems (BRSs) and model checking techniques for modeling and verifying the interaction behaviours of SLA-based cloud computing systems. In the first phase of this approach, we address the modeling of the static structure and the dynamic behavior of cloud systems using BRSs. We show how bigraphs enable the description of the different cloud entities, including cloud actors, cloud services, Service Level Agreements (SLAs), the diversity of their properties, and the complex interactions and dependencies among them. Furthermore, we propose a four-stages SLA lifecycle, and define a set of bigraphical reaction rules to abstract these stages and model the dynamic nature of the cloud. The second phase of this approach verifies that the behavior of services and cloud actors will cope with the agreed SLA terms during the lifecycle of the SLA. We map the proposed bigraphical models into SMV descriptions. Then, we express the interaction behaviors as a set of liveness and safety properties using Linear Temporal Logic (LTL) and Computation Tree Logic (CTL) formulas, and we use the NuSMV model checker to verify them. Finally, we define a case study on which we illustrate the application of our proposed approach.

Formalizing and simulating cross-layer elasticity strategies in Cloud systems

Clouds are complex systems that provide computing resources in an elastic way. Elasticity allows their adaptation to input workloads by (de)provisioning resources as the demand rises and drops. Given the numerous overlapping factors that impact their elasticity and the unpredictable nature of the workload, providing accurate action plans to manage Cloud elasticity is a particularly challenging task. In this paper, we propose a formal approach based on bigraphical reactive systems to model Cloud structures and their elastic behavior. We design cross-layer elasticity strategies which operate at application and infrastructure Cloud layers to manage the elastic adaptations. We encode the elastic behaviors in Rewriting logic, through the Maude framework, to enable their generic executability. We provide a qualitative verification of the designed behaviors’ correctness with a model-checking technique supported by the linear temporal logic. Finally, we provide a tooled simulation-based methodology, through the Queuing theory, to conduct a quantitative analysis of the designed elasticity strategies.

Guest Editorial: Adaptive and Reconfigurable Service‐Oriented, Cloud and Virtualised Architectures

The concept of adaptive and reconfigurable Service Oriented Architecture (SOA) has been introduced in order to describe architectures that exhibit emerging functional and non-functional properties in changing contexts. An adaptive and reconfigurable can repair itself if any execution problem occurs, in order to successfully complete its own execution, while respecting functional and non-functional agreements. In the design of an adaptive and reconfigurable SOA, several aspects have to be considered. For instance, the architecture components should be able to predict and to detect degradations and failures as soon as possible and to enact suitable recovery actions such as scaling-up and scaling-out of virtual execution resources. Moreover, different non-functional service-level requirements might be considered in order to complete the execution in case of a predicted imminent or observed occurring failure. Contributions are devoted to the design and the implementation of adaptive and reconfigurable and related Cloud applications. The issue contains five papers related to the foundations of SOA and Cloud and the tools and applications for and Cyber-Physical environments. Service Oriented Architecture and Cloud Computing E2SM: A Security tool for Adaptive Cloud-based Service-Oriented Applications by Takoua Abdellatif proposes an End-to-end Security Model (E2SM) that aims to protect data confidentiality in adaptive cloud-based applications. Whereas Leah Mutanu and Gerald Kotonya study the key factors that influence runtime adaptation in service-oriented architectures, and examines how well they are addressed in 29 adaptation approaches intended to support service-oriented systems in the paper entitled What, Where, When, How and Right of Runtime Adaptation in Service-Oriented Systems. The paper entitled and Analyzing Elastic Strategies in Cloud by Khaled Khebbeb et al. proposes a Bigraphical Reactive Systems based approach to provide a formal modelling of Cloud systems' structure using bigraphs, and their elastic behaviours using bigraphical reaction rules. Smart and Cyber-Physical environments and Verifying Time-aware Processes for Cyber-Physical Environments by Imen Graja et al. proposes to extend Business Process Modeling Notation to support the various Cyber-physical system concepts and properties. The paper entitled and Safe Self-Adaption of Connected Devices Based on Discrete Controllers by Arthur Gatouillat et al. proposes a self-adaptation framework to deal with changes and takes into account storage, computational and communication constraints.

Timed CTL checking of time critical cloud applications using timed bigraphs

Controlling cloud resources provisioning for time critical applications is crucial to meet required quality of service (QoS) of modern applications. Both computational resources capabilities and network bandwidth should be considered to accurately serve practical needs, while complying relevant constraints. The objective of this work is to show how to add time constructs to the bigraphical reactive systems (BRSs) formalism, in order to describe and analyse the execution of cloud applications having temporal constraints. In particular, we are interested in the cloud resource allocation problem to meet end user requests while considering network deadline, as well as the service processing time. The proposed time-aware BRS model is then integrated in the Real-Time Maude language and its TCTL model checker in order to obtain an executable and analysable specification of cloud applications having temporal constraints.

A Bigraphical Reactive Systems with Sharing for modeling Wireless Mesh Networks

Recently, various types of wireless networks and mobile communication technologies have emerged; particularly the Wireless Mesh Networks (WMN) improving significantly the capacities of mobile communications. This paper aims to propose new insights on theoretical aspects of WMN by giving a novel modeling approach.We lean on formal methods to show how to define a precise semantics for WMN and how to formally analyze their routing protocols. We combine the logical reflection of Maude language and the hierarchical structure of the Bigraphical Reactive Systems (BRS) to provide an executable formal model for WMN. This model, called Bis-WMN specifies both the WMN topology and any behavior which may be observed during its routing process. Some inherent properties have been then checked with the LTL model checker of Maude.

Executing bigraphical reactive systems

In order to enable experimentations and simulations of bigraphs, we need an implementation of their dynamics. 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.

On the Interplay Between Cyber and Physical Spaces for Adaptive Security

Ubiquitous computing is resulting in a proliferation of cyber-physical systems that host or manage valuable physical and digital assets. These assets can be harmed by malicious agents through both cyber-enabled or physically-enabled attacks, particularly ones that exploit the often ignored interplay between the cyber and physical world. The explicit representation of spatial topology is key to supporting adaptive security policies. In this paper we explore the use of Bigraphical Reactive Systems to model the topology of cyber and physical spaces and their dynamics. We utilise such models to perform speculative threat analysis through model checking to reason about the consequences of the evolution of topological configurations on the satisfaction of security requirements. We further propose an automatic planning technique to identify an adaptation strategy enacting security policies at runtime to prevent, circumvent, or mitigate possible security requirements violations. We evaluate our approach using a case study concerned with countering insider threats in a building automation system.

Describing correct deployment architectures based on a bigraphical multi-scale modeling approach

In this paper, we propose a formal approach supporting the correct description of deployment architectures and their reconfigurations. According to defined models, correct deployment architectures are generated and one of them is selected to be deployed. This generation process is based on a multi-scale modeling approach adopting Bigraphs and Bigraphical Reactive Systems as a modeling language. In fact, the architecture of a scale is refined by adding the components of the next scale. Then, the obtained architecture is in turn refined and so on, until reaching the last scale. The transition between scales is performed through applying refinement rules. Based on correct by design, the refinement process is executed on a correct scale architecture (respects the defined models) by applying correct rules. So, we ensure that the generated scale architectures are correct. Finally, our approach is illustrated through the case study Smart Home.

Big-CAF: a bigraphical-generic cloud architecture framework

Cloud computing is an emerging paradigm that enhances grid computing but in the sense of the utility computing principle. Hence, it attracts more attention in both industry and academia. However, there are still many obstacles that are slowing down its adoption and growth. An important and challenging issue in this area is how to associate a clear semantic to cloud architecture concepts. Based on BRS (Bigraphical Reactive Systems) theory, the paper presents a formal framework that provides mathematical definitions of main elements involved in a cloud architecture, specifying its static structure and dynamic evolution. As a consequence of this formalisation, a practical implementation based on Maude and its model checker is proposed to ensure the correctness of cloud systems.

Big-CAF: a bigraphical-generic cloud architecture framework

Cloud computing is an emerging paradigm that enhances grid computing but in the sense of the utility computing principle. Hence, it attracts more attention in both industry and academia. However, there are still many obstacles that are slowing down its adoption and growth. An important and challenging issue in this area is how to associate a clear semantic to cloud architecture concepts. Based on BRS (Bigraphical Reactive Systems) theory, the paper presents a formal framework that provides mathematical definitions of main elements involved in a cloud architecture, specifying its static structure and dynamic evolution. As a consequence of this formalisation, a practical implementation based on Maude and its model checker is proposed to ensure the correctness of cloud systems.

Encoding Bigraphical Reactive Systems into Graph Transformation Systems

In this paper, we present a solution for executing bigraphical reactive systems based on an investigation on graph transformation systems. For this, we encode a bigraph into a ranked graph. This encoding is ensured, formally, by defining a faithful functor that allows to move from bigraph category to ranked graph category. Then, we show that reaction rules can be simulated with graph rules.

A bigraphical model for specifying cloud-based elastic systems and their behaviour

The few recent years have witnessed the appearance of a new kind of self-adaptive systems called cloud based-elastic systems. These systems are particularly appealing for their ability to maintain a decent quality of service and reduce a system’s operating cost at the same time. They achieve this by dynamically adjusting resources allocation in terms of elasticity. Meanwhile, complexity of structural and behavioural aspects related to cloud-based elastic systems increase the difficulty of designing and developing such systems. In this paper, we address this challenge by proposing a formal approach based on bigraphical reactive systems for modelling both structural and behavioural aspects of cloud-based elastic systems. In particular, we represent their behaviour in terms of client/application interactions and elasticity methods at different levels using bigraphical reaction rules. The feasibility of the proposed approach is illustrated through a motivating example running on the top of an Amazon Elastic Compute Cloud (EC2) infrastructure.

A bigraph-based framework for specification and analysis of context-aware systems

Context-aware systems refer to a particular class of ubiquitous computing in which, systems are able to sense environmental information and adapt their behaviour accordantly. However, the key challenge in the ubiquitous computing lies in providing a consistent model in order to deal with the increasing complexity and variety of context-aware systems. In this paper, we present a rigorous approach based on bigraphical reactive systems for modelling the main features of context-aware systems. The proposed approach provides a clear separation between the part of the system which is affected by the context and the remaining part. Moreover, it is equipped with a domain-specific tool, so-called BigCAS-Tool, which supports the modelling and execution of context-aware systems models. BigCAS-Tool features and capabilities are illustrated through a case study of a traffic sign recognition system.

Bigraphs with sharing

Bigraphical Reactive Systems (BRS) were designed by Milner as a universal formalism for modelling systems that evolve in time, locality, co-locality and connectivity. But the underlying model of location (the place graph) is a forest, which means there is no straightforward representation of locations that can overlap or intersect. This occurs in many domains, for example in wireless signalling, social interactions and audio communications. Here, we define bigraphs with sharing, which solves this problem by an extension of the basic formalism: we define the place graph as a directed acyclic graph, thus allowing a natural representation of overlapping or intersecting locations. We give a complete presentation of the theory of bigraphs with sharing, including a categorical semantics, algebraic properties, and several essential procedures for computation: bigraph with sharing matching, a SAT encoding of matching, and checking a fragment of the logic BiLog. We show that matching is an instance of the NP-complete sub-graph isomorphism problem and our approach based on a SAT encoding is also efficient for standard bigraphs. We give an overview of BigraphER (Bigraph Evaluator & Rewriting), an efficient implementation of bigraphs with sharing that provides manipulation, simulation and visualisation. The matching engine is based on the SAT encoding of the matching algorithm. Examples from the 802.11 CSMA/CA RTS/CTS protocol and a network management support system illustrate the applicability of the new theory.