[FKN+11] Vojtěch Forejt, Marta Kwiatkowska, Gethin Norman, David Parker and Hongyang Qu. Quantitative Multi-Objective Verification for Probabilistic Systems. In Proc. 17th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS'11), volume 6605 of LNCS, pages 112-127, Springer. March 2011. [pdf] [bib] [Presents multi-objective and assume-guarantee verification techniques for probabilistic automata, implemented as an extension of PRISM.]
Abstract. We present a verification framework for analysing multiple quantitative objectives of systems that exhibit both nondeterministic and stochastic behaviour. These systems are modelled as probabilistic automata, enriched with cost or reward structures that capture, for example, energy usage or performance metrics. Quantitative properties of these models are expressed in a specification language that incorporates probabilistic safety and liveness properties, expected total cost or reward, and supports multiple objectives of these types. We propose and implement an efficient verification framework for such properties and then present two distinct applications of it: firstly, controller synthesis subject to multiple quantitative objectives; and, secondly, quantitative compositional verification. The practical applicability of both approaches is illustrated with experimental results from several large case studies.