Abstract: The automation of power grids by means of supervisory control and data acquisition (SCADA) systems has led to an improvement of power grid operations and functionalities but also to pervasive cyber interdependencies between power grids and telecommunication networks. Many power grid services are increasingly depending upon the adequate functionality of SCADA system which in turn strictly depends on the adequate functionality of its communication infrastructure. We propose to tackle the SCADA risk analysis by means of different and heterogeneous modeling techniques and software tools. We demonstrate the applicability of our approach through a case study on an actual SCADA system for an electrical power distribution grid. The modeling techniques we discuss aim at providing a probabilistic dependability analysis, followed by a worst case analysis in presence of malicious attacks and a real-time performance evaluation.

Abstract: We present two OBDD based model checking algorithms for the verification of Nash equilibria in finite state mechanisms modeling Multiple Administrative Domains (MAD) distributed systems with possibly colluding agents (coalitions) and with possibly faulty or malicious nodes (Byzantine agents). Given a finite state mechanism, a proposed protocol for each agent and the maximum sizes f for Byzantine agents and q for agents collusions, our model checkers return Pass if the proposed protocol is an ε-f-q-Nash equilibrium, i.e. no coalition of size up to q may have an interest greater than ε in deviating from the proposed protocol when up to f Byzantine agents are present, Fail otherwise. We implemented our model checking algorithms within the NuSMV model checker: the first one explicitly checks equilibria for each coalition, while the second represents symbolically all coalitions. We present experimental results showing their effectiveness for moderate size mechanisms. For example, we can verify coalition Nash equilibria for mechanisms which corresponding normal form games would have more than $5 \times 10^21$ entries. Moreover, we compare the two approaches, and the explicit algorithm turns out to outperform the symbolic one. To the best of our knowledge, no model checking algorithm for verification of Nash equilibria of mechanisms with coalitions has been previously published.

Abstract: The modeling and analysis of hybrid systems is a recent and challenging research area which is actually dominated by two main lines: a functional analysis based on the description of the system in terms of discrete state (hybrid) automata (whose goal is to ascertain conformity and reachability properties), and a stochastic analysis (whose aim is to provide performance and dependability measures). This paper investigates a unifying view between formal methods and stochastic methods by proposing an analysis methodology of hybrid systems based on Fluid Petri Nets (FPNs). FPNs can be analyzed directly using appropriate tools. Our paper shows that the same FPN model can be fed to different functional analyzers for model checking. In order to extensively explore the capability of the technique, we have converted the original FPN into languages for discrete as well as hybrid as well as stochastic model checkers. In this way, a first comparison among the modeling power of well known tools can be carried out. Our approach is illustrated by means of a ’real world’ hybrid system: the temperature control system of a co-generative plant.