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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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Federico Mari, Igor Melatti, Ivano Salvo, and Enrico Tronci. "From Boolean Relations to Control Software." In Proceedings of ICSEA 2011, The Sixth International Conference on Software Engineering Advances, 528–533. ThinkMind, 2011. ISSN: 978-1-61208-165-6. Notes: Best Paper Award.
Abstract: Many software as well digital hardware automatic synthesis methods define the set of implementations meeting the given system specifications with a boolean relation K. In such a context a fundamental step in the software (hardware) synthesis process is finding effective solutions to the functional equation defined by K. This entails finding a (set of) boolean function(s) F (typically represented using OBDDs, Ordered Binary Decision Diagrams) such that: 1) for all x for which K is satisfiable, K(x, F(x)) = 1 holds; 2) the implementation of F is efficient with respect to given implementation parameters such as code size or execution time. While this problem has been widely studied in digital hardware synthesis, little has been done in a software synthesis context. Unfortunately the approaches developed for hardware synthesis cannot be directly used in a software context. This motivates investigation of effective methods to solve the above problem when F has to be implemented with software. In this paper we present an algorithm that, from an OBDD representation for K, generates a C code implementation for F that has the same size as the OBDD for F and a WCET (Worst Case Execution Time) linear in nr, being n = |x| the number of input arguments for functions in F and r the number of functions in F.
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Federico Mari, Igor Melatti, Ivano Salvo, and Enrico Tronci. "Control Software Visualization." In Proceedings of INFOCOMP 2012, The Second International Conference on Advanced Communications and Computation, 15–20. ThinkMind, 2012. ISSN: 978-1-61208-226-4.
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