Abstract: To support Model Based Design of Cyber-Physical Systems (CPSs) many simulation based approaches to System Level Formal Verification (SLFV) have been devised. Basically, these are Bounded Model Checking approaches (since simulation horizon is of course bounded) relying on simulators to compute the system dynamics and thereby verify the given system properties. The main obstacle to simulation based SLFV is the large number of simulation scenarios to be considered and thus the huge amount of simulation time needed to complete the verification task. To save on computation time, simulation based SLFV approaches exploit the capability of simulators to save and restore simulation states. Essentially, such a time saving is obtained by optimising the simulation script defining the simulation activity needed to carry out the verification task. Although such approaches aim to (bounded) formal verification, as a matter of fact, the proof of correctness of the methods to optimise simulation scripts basically relies on an intuitive semantics for simulation scripting languages. This hampers the possibility of formally showing that the optimisations introduced to speed up the simulation activity do not actually omit checking of relevant behaviours for the system under verification. The aim of this paper is to fill the above gap by presenting an operational semantics for simulation scripting languages and by proving soundness and completeness properties for it. This, in turn, enables formal proofs of equivalence between unoptimised and optimised simulation scripts.

Abstract: We present a symbolic model checking algorithm for verification of Nash equilibria in finite state mechanisms modeling Multiple Administrative Domains (MAD) distributed systems. Given a finite state mechanism, a proposed protocol for each agent and an indifference threshold for rewards, our model checker returns PASS if the proposed protocol is a Nash equilibrium (up to the given indifference threshold) for the given mechanism, FAIL otherwise. We implemented our model checking algorithm inside the NuSMV model checker and present experimental results showing its effectiveness for moderate size mechanisms. For example, we can handle mechanisms which corresponding normal form games would have more than $10^20$ entries. To the best of our knowledge, no model checking algorithm for verification of mechanism Nash equilibria has been previously published.

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.