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Enrico Tronci, Giuseppe Della Penna, Benedetto Intrigila, and Marisa Venturini Zilli. "A Probabilistic Approach to Automatic Verification of Concurrent Systems." In 8th Asia-Pacific Software Engineering Conference (APSEC), 317–324. Macau, China: IEEE Computer Society, 2001. ISSN: 0-7695-1408-1. DOI: 10.1109/APSEC.2001.991495.
Abstract: The main barrier to automatic verification of concurrent systems is the huge amount of memory required to complete the verification task (state explosion). In this paper we present a probabilistic algorithm for automatic verification via model checking. Our algorithm trades space with time. In particular, when memory is full because of state explosion our algorithm does not give up verification. Instead it just proceeds at a lower speed and its results will only hold with some arbitrarily small error probability. Our preliminary experimental results show that by using our probabilistic algorithm we can typically save more than 30% of RAM with an average time penalty of about 100% w.r.t. a deterministic state space exploration with enough memory to complete the verification task. This is better than giving up the verification task because of lack of memory.
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Federico Mari, Igor Melatti, Ivano Salvo, Enrico Tronci, Lorenzo Alvisi, Allen Clement, and Harry Li. "Model Checking Nash Equilibria in MAD Distributed Systems." In FMCAD '08: Proceedings of the 2008 International Conference on Formal Methods in Computer-Aided Design, edited by A. Cimatti and R. Jones, 1–8. Piscataway, NJ, USA: IEEE Press, 2008. ISSN: 978-1-4244-2735-2. DOI: 10.1109/FMCAD.2008.ECP.16.
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.
Keywords: Model Checking, MAD Distributed System, Nash Equilibrium
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Giuseppe Della Penna, Benedetto Intrigila, Enrico Tronci, and Marisa Venturini Zilli. "Exploiting Transition Locality in the Disk Based Mur$\varphi$ Verifier." In 4th International Conference on Formal Methods in Computer-Aided Design (FMCAD), edited by M. Aagaard and J. W. O'Leary, 202–219. Lecture Notes in Computer Science 2517. Portland, OR, USA: Springer, 2002. ISSN: 3-540-00116-6. DOI: 10.1007/3-540-36126-X_13.
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$\varphi$.
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