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A recurrent task in coordinated systems is managing (estimating, predicting, or controlling) signals that vary in space, such as distributed sensed data or computation outcomes. Especially in large-scale settings, the problem can be addressed through decentralised and situated computing systems: nodes can locally sense, process, and act upon signals, and coordinate with neighbours to implement collective strategies. Accordingly, in this work we devise distributed coordination strategies for the estimation of a spatial phenomenon through collaborative adaptive sampling. Our design is based on the idea of dynamically partitioning space into regions that compete and grow/shrink to provide accurate aggregate sampling. Such regions hence define a sort of virtualised space that is "fluid", since its structure adapts in response to pressure forces exerted by the underlying phenomenon. We provide an adaptive sampling algorithm in the field-based coordination framework, and prove it is self-stabilising and locally optimal. Finally, we verify by simulation that the proposed algorithm effectively carries out a spatially adaptive sampling while maintaining a tuneable trade-off between accuracy and efficiency.

Recent works in contexts like the Internet of Things (IoT) and large-scale Cyber-Physical Systems (CPS) propose the idea of programming distributed systems by focussing on their global behaviour across space and time. In this view, a potentially vast and heterogeneous set of devices is considered as an "aggregate" to be programmed as a whole, while abstracting away the details of individual behaviour and exchange of messages, which are expressed declaratively. One such a paradigm, known as aggregate programming, builds on computational models inspired by field-based coordination. Existing models such as the field calculus capture interaction with neighbours by a so-called "neighbouring field" (a map from neighbours to values). This requires ad-hoc mechanisms to smoothly compose with standard values, thus complicating programming and introducing clutter in aggregate programs, libraries and domain-specific languages (DSLs). To address this key issue we introduce the novel notion of "computation against a neighbour", whereby the evaluation of certain subexpressions of the aggregate program are affected by recent corresponding evaluations in neighbours. We capture this notion in the neighbours calculus (NC), a new field calculus variant which is shown to smoothly support declarative specification of interaction with neighbours, and correspondingly facilitate the embedding of field computations as internal DSLs in common general-purpose programming languages -- as exemplified by a Scala implementation, called ScaFi. This paper formalises NC, thoroughly compares it with respect to the classic field calculus, and shows its expressiveness by means of a case study in edge computing, developed in ScaFi.

Supported by current socio-scientific trends, programming the global behaviour of whole computational collectives makes for great opportunities, but also significant challenges. Recently, aggregate computing has emerged as a prominent paradigm for so-called collective adaptive systems programming. To shorten the gap between such research endeavours and mainstream software development and engineering, we present ScaFi, a Scala toolkit providing an internal domain-specific language, libraries, a simulation environment, and runtime support for practical aggregate computing systems development.

Emerging application scenarios, such as cyber-physical systems (CPSs), the Internet of Things (IoT), and edge computing, call for coordination approaches addressing openness, self-adaptation, heterogeneity, and deployment agnosticism. Field-based coordination is one such approach, promoting the idea of programming system coordination declaratively from a global perspective, in terms of functional manipulation and evolution in "space and time" of distributed data structures called fields. More specifically regarding time, in field-based coordination (as in many other distributed approaches to coordination) it is assumed that local activities in each device are regulated by a fair and unsynchronised fixed clock working at the platform level. In this work, we challenge this assumption, and propose an alternative approach where scheduling is programmed in a natural way (along with usual field-based coordination) in terms of causality fields, each enacting a programmable distributed notion of a computation "cause" (why and when a field computation has to be locally computed) and how it should change across time and space. Starting from low-level platform triggers, such causality fields can be organised into multiple layers, up to high-level, collectively-computed time abstractions, to be used at the application level. This reinterpretation of time in terms of articulated causality relations allows us to express what we call "time-fluid" coordination, where scheduling can be finely tuned so as to select the triggers to react to, generally allowing to adaptively balance performance (system reactivity) and cost (resource usage) of computations. We formalise the proposed scheduling framework for field-based coordination in the context of the field calculus, discuss an implementation in the aggregate computing framework, and finally evaluate the approach via simulation on several case studies.

Runtime verification is a computing analysis paradigm based on observing a system at runtime (to check its expected behaviour) by means of monitors generated from formal specifications. Distributed runtime verification is runtime verification in connection with distributed systems: it comprises both monitoring of distributed systems and using distributed systems for monitoring. Aggregate computing is a programming paradigm based on a reference computing machine that is the aggregate collection of devices that cooperatively carry out a computational process: the details of behaviour, position and number of devices are largely abstracted away, to be replaced with a space-filling computational environment. In this position paper we argue, by means of simple examples, that aggregate computing is particularly well suited for implementing distributed monitors. Our aim is to foster further research on how to generate aggregate computing monitors from suitable formal specifications.

Field-based coordination has been proposed as a model for coordinating collective adaptive systems, promoting a view of distributed computations as functions manipulating data structures spread over space and evolving over time, called computational fields. The field calculus is a formal foundation for field computations, providing specific constructs for evolution (time) and neighbor interaction (space), which are handled by separate operators (called rep and nbr, respectively). This approach, however, intrinsically limits the speed of information propagation that can be achieved by their combined use. In this paper, we propose a new field-based coordination operator called share, which captures the space-time nature of field computations in a single operator that declaratively achieves: (i) observation of neighbors' values; (ii) reduction to a single local value; and (iii) update and converse sharing to neighbors of a local variable. We show that for an important class of self-stabilising computations, share can replace all occurrences of rep and nbr constructs. In addition to conceptual economy, use of the share operator also allows many prior field calculus algorithms to be greatly accelerated, which we validate empirically with simulations of frequently used network propagation and collection algorithms.

Collecting statistic from graph-based data is an increasingly studied topic in the data mining community. We argue that these statistics have great value as well in dynamic IoT contexts: they can support complex computational activities involving distributed coordination and provision of situation recognition. We show that the HyperANF algorithm for calculating the neighbourhood function of vertices of a graph naturally allows for a fully distributed and asynchronous implementation, thanks to a mapping to the field calculus, a distribution model proposed for collective adaptive systems. This mapping gives evidence that the field calculus framework is well-suited to accommodate massively parallel computations over graphs. Furthermore, it provides a new "self-stabilising" building block which can be used in aggregate computing in several contexts, there including improved leader election or network vulnerabilities detection.

The engineering of large-scale cyber-physical systems (CPS) increasingly relies on principles from self-organisation and collective computing, enabling these systems to cooperate and adapt in dynamic environments. CPS engineering also often leverages digital twins that provide synchronised logical counterparts of physical entities. In contrast, sensor networks rely on the different but related concept of virtual device that provides an abstraction of a group of sensors. In this work, we study how such concepts can contribute to the engineering of self-organising CPSs. To that end, we analyse the concepts and devise modelling constructs, distinguishing between identity correspondence and execution relationships. Based on this analysis, we then contribute to the novel concept of “collective digital twin” (CDT) that captures the logical counterpart of a collection of physical devices. A CDT can also be “augmented” with purely virtual devices, which may be exploited to steer the self-organisation process of the CDT and its physical counterpart. We underpin the novel concept with experiments in the context of the pulverisation framework of aggregate computing, showing how augmented CDTs provide a holistic, modular, and cyber-physically integrated system view that can foster the engineering of self-organising CPSs.

Research and technology developments on autonomous agents and autonomic computing promote a vision of artificial systems that are able to resiliently manage themselves and autonomously deal with issues at runtime in dynamic environments. Indeed, autonomy can be leveraged to unburden humans from mundane tasks (cf. driving and autonomous vehicles), from the risk of operating in unknown or perilous environments (cf. rescue scenarios), or to support timely decision-making in complex settings (cf. data-centre operations). Beyond the results that individual autonomous agents can carry out, a further opportunity lies in the collaboration of multiple agents or robots. Emerging macro-paradigms provide an approach to programming whole collectives towards global goals. Aggregate computing is one such paradigm, formally grounded in a calculus of computational fields enabling functional composition of collective behaviours that could be proved, under certain technical conditions, to be self-stabilising. In this work, we address the concept of collective autonomy, i.e., the form of autonomy that applies at the level of a group of individuals. As a contribution, we define an agent control architecture for aggregate multi-agent systems, discuss how the aggregate computing framework relates to both individual and collective autonomy, and show how it can be used to program collective autonomous behaviour. We exemplify the concepts through a simulated case study, and outline a research roadmap towards reliable aggregate autonomy.

One of the difficulties in developing collective adaptive systems is the challenge of simultaneously engineering both the desired resilient behaviour of the collective and the details of its implementation on individual devices. Aggregate computing simplifies this problem by separating these aspects into different layers of abstraction by means of a unifying notion of computational field and a functional computational model. We review the state of the art in aggregate computing, discuss the various resiliency properties it supports, and develop a roadmap of foundational problems still needing to be addressed in the continued development of this emerging discipline.

Emerging cyber-physical systems, such as robot swarms, crowds of augmented people, and smart cities, require well-crafted self-organizing behavior to properly deal with dynamic environments and pervasive disturbances. However, the infrastructures providing networking and computing services to support these systems are becoming increasingly complex, layered and heterogeneous—consider the case of the edge–fog–cloud interplay. This typically hinders the application of self-organizing mechanisms and patterns, which are often designed to work on flat networks. To promote reuse of behavior and flexibility in infrastructure exploitation, we argue that self-organizing logic should be largely independent of the specific application deployment. We show that this separation of concerns can be achieved through a proposed “pulverization approach”: the global system behavior of application services gets broken into smaller computational pieces that are continuously executed across the available hosts. This model can then be instantiated in the aggregate computing framework, whereby self-organizing behavior is specified compositionally. We showcase how the proposed approach enables expressing the application logic of a self-organizing cyber-physical system in a deployment-independent fashion, and simulate its deployment on multiple heterogeneous infrastructures that include cloud, edge, and LoRaWAN network elements.

Emerging network scenarios require the development of solid large-scale situated systems. Unfortunately, the diffusion/aggregation computational processes therein often introduce a source of complexity that hampers predictability of the overall system behaviour. Computational fields have been introduced to help engineering such systems: they are spatially distributed data structures designed to adapt their shape to the topology of the underlying (mobile) network and to the events occurring in it, with notable applications to pervasive computing, sensor networks, and mobile robots. To assure behavioural correctness, namely, correspondence of micro-level specification (single device behaviour) with macro-level behaviour (resulting global spatial pattern), we investigate the issue of self-stabilisation for computational fields. We present a tiny, expressive, and type-sound calculus of computational fields, and define sufficient conditions for self-stabilisation, defined as the ability to react to changes in the environment finding a new stable state in finite time. A type-based approach is used to provide a correct checking procedure for self-stabilisation.