Abstract: We present an algorithm that given a Discrete Time Linear Hybrid System returns a correct-by-construction software implementation K for a (near time optimal) robust quantized feedback controller for along with the set of states on which K is guaranteed to work correctly (controllable region). Furthermore, K has a Worst Case Execution Time linear in the number of bits of the quantization schema.

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 main obstruction to automatic verification of Finite State Systems is the huge amount of memory required to complete the verification task (state explosion). This motivates research on distributed as well as disk based verification algorithms. In this paper we present a disk based Breadth First Explicit State Space Exploration algorithm as well as an implementation of it within the Mur$\varphi$ verifier. Our algorithm exploits transition locality (i.e. the statistical fact that most transitions lead to unvisited states or to recently visited states) to decrease disk read accesses thus reducing the time overhead due to disk usage. A disk based verification algorithm for Mur$\varphi$ has been already proposed in the literature. To measure the time speed up due to locality exploitation we compared our algorithm with such previously proposed algorithm. Our experimental results show that our disk based verification algorithm is typically more than 10 times faster than such previously proposed disk based verification algorithm. To measure the time overhead due to disk usage we compared our algorithm with RAM based verification using the (standard) Mur$\varphi$ verifier with enough memory to complete the verification task. Our experimental results show that even when using 1/10 of the RAM needed to complete verification, our disk based algorithm is only between 1.4 and 5.3 times (3 times on average) slower than (RAM) Mur$\varphi$ with enough RAM memory to complete the verification task at hand. Using our disk based Mur$\varphi$ we were able to complete verification of a protocol with about $10^9$ reachable states. This would require more than 5 gigabytes of RAM using RAM based Mur$\varphi$.

Abstract: In this paper we present an explicit disk based verification algorithm for Probabilistic Systems defining discrete time/finite state Markov Chains. Given a Markov Chain and an integer k (horizon), our algorithm checks whether the probability of reaching an error state in at most k steps is below a given threshold. We present an implementation of our algorithm within a suitable extension of the Mur$\varphi$ verifier. We call the resulting probabilistic model checker FHP-Mur$\varphi$ (Finite Horizon Probabilistic Mur$\varphi$). We present experimental results comparing FHP-Mur$\varphi$ with (a finite horizon subset of) PRISM, a state-of-the-art symbolic model checker for Markov Chains. Our experimental results show that FHP-Mur$\varphi$ can handle systems that are out of reach for PRISM, namely those involving arithmetic operations on the state variables (e.g. hybrid systems).

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.