From biological systems to cyber-physical systems, monitoring the behavior of such dynamical systems often requires to reason about complex spatio-temporal properties of physical and/or computational entities that are dynamically interconnected and a
rranged in a particular spatial configuration. Spatio-Temporal Reach and Escape Logic (STREL) is a recent logic-based formal language designed to specify and to reason about spatio-temporal properties. STREL considers each systems entity as a node of a dynamic weighted graph representing their spatial arrangement. Each node generates a set of mixed-analog signals describing the evolution over time of computational and physical quantities characterising the nodes behavior. While there are offline algorithms available for monitoring STREL specifications over logged simulation traces, here we investigate for the first time an online algorithm enabling the runtime verification during the systems execution or simulation. Our approach extends the original framework by considering imprecise signals and by enhancing the logics semantics with the possibility to express partial guarantees about the conformance of the systems behavior with its specification. Finally, we demonstrate our approach in a real-world environmental monitoring case study.
Collective adaptive systems (CAS) consist of many heterogeneous components typically organised in groups. These entities interact with each other by adapting their behaviour to pursue individual or collective goals. The distribution of system entitie
s determines a space that can be either physical or logical. The former is defined in terms of a physical relation among components. The latter depends on some logical relations such as being part of the same group. For these systems, specification and verification of spatial properties play a fundamental role to understand their behaviour and to support their design. Recently, different tools and languages have been introduced to specify and verify the properties of space. However, these formalisms are mainly based on graphs. This does not permit considering higher-order relations such as surfaces or volumes. In this work, we propose a spatial logic interpreted on simplicial complexes. These are topological objects able to represent surfaces and volumes efficiently and that generalise graphs with higher-order edges. The expressiveness of the proposed spatial logic is studied in terms of bisimulation and branching bisimulation relations defined over simplicial complexes. Finally, we discuss how the satisfaction of logical formulas can be verified by a correct and complete algorithm.
We present MoonLight, a tool for monitoring temporal and spatio-temporal properties of mobile and spatially distributed cyber-physical systems (CPS). In the proposed framework, space is represented as a weighted graph, describing the topological conf
igurations in which the single CPS entities (nodes of the graph) are arranged. Both nodes and edges have attributes modelling physical and logical quantities that can change in time. MoonLight is implemented in Java and supports the monitoring of Spatio-Temporal Reach and Escape Logic (STREL). MoonLight can be used as a standalone command line tool, as a Java API, or via Matlab interface. We provide here some examples using the Matlab interface and we evaluate the tool performance also by comparing with other tools specialized in monitoring only temporal properties.
Cyber-Physical Systems~(CPS) consist of collaborative, networked and tightly intertwined computational (logical) and physical components, each operating at different spatial and temporal scales. Hence, the spatial and temporal requirements play an es
sential role for their correct and safe execution. Furthermore, the local interactions among the system components result in global spatio-temporal emergent behaviors often impossible to predict at the design time. In this work, we pursue a complementary approach by introducing STREL a novel spatio-temporal logic that enables the specification of spatio-temporal requirements and their monitoring over the execution of mobile and spatially distributed CPS. Our logic extends the Signal Temporal Logic with two novel spatial operators reach and escape from which is possible to derive other spatial modalities such as everywhere, somewhere and surround. These operators enable a monitoring procedure where the satisfaction of the property at each location depends only on the satisfaction of its neighbours, opening the way to future distributed online monitoring algorithms. We propose both a qualitative and quantitative semantics based on constraint semirings, an algebraic structure suitable for constraint satisfaction and optimisation. We prove that, for a subclass of models, all the spatial properties expressed with reach and escape, using euclidean distance, satisfy all the model transformations using rotation, reflection and translation. Finally, we provide an offline monitoring algorithm for STREL and, to demonstrate the feasibility of our approach, we show its application using the monitoring of a simulated mobile ad-hoc sensor network as running example.
We propose a process calculus, named AbC, to study the behavioural theory of interactions in collective-adaptive systems by relying on attribute-based communication. An AbC system consists of a set of parallel components each of which is equipped wit
h a set of attributes. Communication takes place in an implicit multicast fashion, and interaction among components is dynamically established by taking into account connections as determined by predicates over their attributes. The structural operational semantics of AbC is based on Labeled Transition Systems that are also used to define bisimilarity between components. Labeled bisimilarity is in full agreement with a barbed congruence, defined by simple basic observables and context closure. The introduced equivalence is used to study the expressiveness of AbC in terms of encoding broadcast channel-based interactions and to establish formal relationships between system descriptions at different levels of abstraction.
Collective adaptive systems are new emerging computational systems consisting of a large number of interacting components and featuring complex behaviour. These systems are usually distributed, heterogeneous, decentralised and interdependent, and are
operating in dynamic and possibly unpredictable environments. Finding ways to understand and design these systems and, most of all, to model the interactions of their components, is a difficult but important endeavour. In this article we propose a language-based approach for programming the interactions of collective-adaptive systems by relying on attribute-based communication; a paradigm that permits a group of partners to communicate by considering their run-time properties and capabilities. We introduce AbC, a foundational calculus for attribute-based communication and show how its linguistic primitives can be used to program a complex and sophisticated variant of the well-known problem of Stable Allocation in Content Delivery Networks. Also other interesting case studies, from the realm of collective-adaptive systems, are considered. We also illustrate the expressive power of attribute-based communication by showing the natural encoding of other existing communication paradigms into AbC.
Coordination is essential for dynamic distributed systems whose components exhibit interactive and autonomous behaviors. Spatially distributed, locally interacting, propagating computational fields are particularly appealing for allowing components t
o join and leave with little or no overhead. Computational fields are a key ingredient of aggregate programming, a promising software engineering methodology particularly relevant for the Internet of Things. In our approach, space topology is represented by a fixed graph-shaped field, namely a network with attributes on both nodes and arcs, where arcs represent interaction capabilities between nodes. We propose a SMuC calculus where mu-calculus- like modal formulas represent how the values stored in neighbor nodes should be combined to update the present node. Fixpoint operations can be understood globally as recursive definitions, or locally as asynchronous converging propagation processes. We present a distributed implementation of our calculus. The translation is first done mapping SMuC programs into normal form, purely iterative programs and then into distributed programs. Some key results are presented that show convergence of fixpoint computations under fair asynchrony and under reinitialization of nodes. The first result allows nodes to proceed at different speeds, while the second one provides robustness against certain kinds of failure. We illustrate our approach with a case study based on a disaster recovery scenario, implemented in a prototype simulator that we use to evaluate the performance of a recovery strategy.
Spatial aspects of computation are becoming increasingly relevant in Computer Science, especially in the field of collective adaptive systems and when dealing with systems distributed in physical space. Traditional formal verification techniques are
well suited to analyse the temporal evolution of programs; however, properties of space are typically not taken into account explicitly. We present a topology-based approach to formal verification of spatial properties depending upon physical space. We define an appropriate logic, stemming from the tradition of topological interpretations of modal logics, dating back to earlier logicians such as Tarski, where modalities describe neighbourhood. We lift the topological definitions to the more general setting of closure spaces, also encompassing discrete, graph-based structures. We extend the framework with a spatial surrounded operator, a propagation operator and with some collective operators. The latter are interpreted over arbitrary sets of points instead of individual points in space. We define efficient model checking procedures, both for the individual and the collective spatial fragments of the logic and provide a proof-of-concept tool.
In open systems, i.e. systems operating in an environment that they cannot control and with components that may join or leave, behaviors can arise as side effects of intensive components interaction. Finding ways to understand and design these system
s and, most of all, to model the interactions of their components, is a difficult but important endeavor. To tackle these issues, we present AbC, a calculus for attribute-based communication. An AbC system consists of a set of parallel agents each of which is equipped with a set of attributes. Communication takes place in an implicit multicast fashion, and interactions among agents are dynamically established by taking into account connections as determined by predicates over the attributes of agents. First, the syntax and the semantics of the calculus are presented, then expressiveness and effectiveness of AbC are demonstrated both in terms of modeling scenarios featuring collaboration, reconfiguration, and adaptation and of the possibility of encoding channel-based interactions and other interaction patterns. Behavioral equivalences for AbC are introduced for establishing formal relationships between different descriptions of the same system.
Two of the most studied extensions of trace and testing equivalences to nondeterministic and probabilistic processes induce distinctions that have been questioned and lack properties that are desirable. Probabilistic trace-distribution equivalence di
fferentiates systems that can perform the same set of traces with the same probabilities, and is not a congruence for parallel composition. Probabilistic testing equivalence, which relies only on extremal success probabilities, is backward compatible with testing equivalences for restricted classes of processes, such as fully nondeterministic processes or generative/reactive probabilistic processes, only if specific sets of tests are admitted. In this paper, n
