Abstract: In critical infrastructures like airports, much care has to be devoted in protecting radio communication networks from external electromagnetic interference. Protection of such mission-critical radio communication networks is usually tackled by exploiting radiogoniometers: at least three suitably deployed radiogoniometers, and a gateway gathering information from them, permit to monitor and localise sources of electromagnetic emissions that are not supposed to be present in the monitored area. Typically, radiogoniometers are connected to the gateway through relay nodes . As a result, some degree of fault-tolerance for the network of relay nodes is essential in order to offer a reliable monitoring. On the other hand, deployment of relay nodes is typically quite expensive. As a result, we have two conflicting requirements: minimise costs while guaranteeing a given fault-tolerance. In this paper, we address the problem of computing a deployment for relay nodes that minimises the overall cost while at the same time guaranteeing proper working of the network even when some of the relay nodes (up to a given maximum number) become faulty (fault-tolerance ). We show that, by means of a computation-intensive pre-processing on a HPC infrastructure, the above optimisation problem can be encoded as a 0/1 Linear Program, becoming suitable to be approached with standard Artificial Intelligence reasoners like MILP, PB-SAT, and SMT/OMT solvers. Our problem formulation enables us to present experimental results comparing the performance of these three solving technologies on a real case study of a relay node network deployment in areas of the Leonardo da Vinci Airport in Rome, Italy.

Abstract: Model-based approaches to the verification of non-terminating Cyber-Physical Systems (CPSs) usually rely on numerical simulation of the System Under Verification (SUV) model under input scenarios of possibly varying duration, chosen among those satisfying given constraints. Such constraints typically stem from requirements (or assumptions) on the SUV inputs and its operational environment as well as from the enforcement of additional conditions aiming at, e.g., prioritising the (often extremely long) verification activity, by, e.g., focusing on scenarios explicitly exercising selected requirements, or avoiding </i>vacuity</i> in their satisfaction. In this setting, the possibility to efficiently sample at random (with a known distribution, e.g., uniformly) within, or to efficiently enumerate (possibly in a uniformly random order) scenarios among those satisfying all the given constraints is a key enabler for the practical viability of the verification process, e.g., via simulation-based statistical model checking. Unfortunately, in case of non-trivial combinations of constraints, iterative approaches like Markovian random walks in the space of sequences of inputs in general fail in extracting scenarios according to a given distribution (e.g., uniformly), and can be very inefficient to produce at all scenarios that are both legal (with respect to SUV assumptions) and of interest (with respect to the additional constraints). For example, in our case studies, up to 91% of the scenarios generated using such iterative approaches would need to be neglected. In this article, we show how, given a set of constraints on the input scenarios succinctly defined by multiple finite memory monitors, a data structure (scenario generator) can be synthesised, from which any-horizon scenarios satisfying the input constraints can be efficiently extracted by (possibly uniform) random sampling or (randomised) enumeration. Our approach enables seamless support to virtually all simulation-based approaches to CPS verification, ranging from simple random testing to statistical model checking and formal (i.e., exhaustive) verification, when a suitable bound on the horizon or an iterative horizon enlargement strategy is defined, as in the spirit of bounded model checking.