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[Kwi07] M. Kwiatkowska. Quantitative Verification: Models, Techniques and Tools. In Proc. 6th joint meeting of the European Software Engineering Conference and the ACM SIGSOFT Symposium on the Foundations of Software Engineering (ESEC/FSE), pages 449-458, ACM Press. September 2007. [pdf] [bib]
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Notes: Copyright: ACM, 2007. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version is at http://portal.acm.org/citation.cfm?doid=1287624.1287688
Abstract. Automated verification is a technique for establishing if certain properties, usually expressed in temporal logic, hold for a system model. The model can be defined using a high-level formalism or extracted directly from software using methods such as abstract interpretation. The verification proceeds through exhaustive exploration of the state-transition graph of the model and is therefore more powerful than testing. Quantitative verification is an analogous technique for establishing quantitative properties of a system model, such as the probability of battery power dropping below minimum, the expected time for message delivery and the expected number of messages lost before protocol termination. Models analysed through this method are typically variants of Markov chains, annotated with costs and rewards that describe resources and their usage during execution. Properties are expressed in temporal logic extended with probabilistic and reward operators. Quantitative verification involves a combination of a traversal of the state-transition graph of the model and numerical computation. This paper gives a brief overview of current research in quantitative verification, concentrating on the potential of the method and outlining future challenges. The modelling approach is described and the usefulness of the methodology illustrated with an example of a real-world protocol standard – Bluetooth device discovery – that has been analysed using the PRISM model checker (www.prismmodelchecker.org).