Optimising Aggregate Monitors for Spatial Logic of Closure Spaces Properties

The advent of highly distributed systems, such as the Internet of Things, has led to the development of distributed systems that require efficient and resilient runtime monitoring. Among the various monitoring techniques, runtime verification is a lightweight verification method that assesses the correctness of a running system concerning a formal specification. In this paper, we investigate the optimization of aggregate monitors, i.e., monitors that operate on ensembles of devices, for properties expressed in Spatial Logic of Closure Spaces (SLCS)--a formal logic designed to reason about spatial relationships between entities in a distributed system. We propose three different algorithms for the implementation of the "somewhere" operator, a key construct in SLCS, and we evaluate their performance through a series of simulations, comparing their convergence time and computational load.