Distributed runtime verification by past-CTL and the field calculus

Recent trends in the engineering of software-intensive systems increasingly promote the adoption of computation at the edge of the network, in the proximity of where sensing and actuation are performed. Applications are executed directly in IoT devices deployed in the physical environment, possibly with the aid of edge servers: there, interactions are essentially based on physical proximity, and communication with the cloud is sporadic if not absent. The challenge of monitoring the execution of such system, by relying on local interactions only, naturally arises. We address this challenge by proposing a rigorous approach to distributed runtime monitoring for space-based networks of devices. We introduce the past-CTL logic, an extension of past-LTL able to express a variety of properties concerning the knowable past of an event. We formally define a procedure to derive, from a past-CTL formula, monitors that can be distributed on each device and whose collective behaviour verifies the validity of the formula at runtime across space and time. This is achieved by relying on the field calculus, a core programming language used to specify the behaviour of a collection of devices by viewing them as an aggregate computing machine, carrying out altogether a distributed computational process. The field calculus is shown to be a convenient language for our goals, since its functional composition approach provides a natural way of translating in a syntax-directed way properties expressed in a given logic into monitors for such properties. We show that the monitor process executing in each single device runs using local memory, message size, and computation time that are all linear in the size of the formula (1 bit per temporal connective). This matches the efficiency of the best available previous results for (non-distributed) monitors derived from past-LTL formulas. Finally, we empirically evaluate the applicability of the approach to sample problems in distributed computing, through simulated experiments with monitors written through a C++ library implementing the field calculus programming constructs.