Stochastic Differential Dynamic Logic for Stochastic Hybrid Programs
Logic is a powerful tool for analyzing and verifying systems, including programs, discrete systems, real-time systems, hybrid systems, and distributed systems. Some applications also have a stochastic behavior, however, either because of fundamental properties of nature, uncertain environments, or simplifications to overcome complexity. Discrete probabilistic systems have been studied using logic. But logic has been chronically underdeveloped in the context of stochastic hybrid systems, i.e., systems with interacting discrete, continuous, and stochastic dynamics. We aim at overcoming this deficiency and introduce a dynamic logic for stochastic hybrid systems. Our results indicate that logic is a promising tool for understanding stochastic hybrid systems and can help taming some of their complexity. We introduce a compositional model for stochastic hybrid systems. We prove adaptivity, càdlàg, and Markov time properties, and prove that the semantics of our logic is measurable. We present compositional proof rules, including rules for stochastic differential equations, and prove soundness.
Unable to display preview. Download preview PDF.
- 3.Cassandras, C.G., Lygeros, J. (eds.): Stochastic Hybrid Systems. CRC, Boca Raton (2006)Google Scholar
- 4.Dutertre, B.: Complete proof systems for first order interval temporal logic. In: LICS, pp. 36–43. IEEE Computer Society, Los Alamitos (1995)Google Scholar
- 18.Bevilacqua, V., Sharykin, R.: Specification and analysis of distributed object-based stochastic hybrid systems. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 460–475. Springer, Heidelberg (2006)Google Scholar
- 22.Platzer, A.: Stochastic differential dynamic logic for stochastic hybrid systems. Tech. Rep. CMU-CS-11-111, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA (2011)Google Scholar
- 24.Pratt, V.R.: Semantical considerations on Floyd-Hoare logic. In: FOCS, pp. 109–121. IEEE, Los Alamitos (1976)Google Scholar