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[Dic14] M. Diciolla. Quantitative Verification of Real-Time Properties with Application to Medical Devices. Ph.D. thesis, Department of Computer Science, University of Oxford. 2014. [pdf] [bib]
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Abstract. Probabilistic model checking is a powerful technique used to ensure the correct functioning of systems which exhibit real-time and stochastic behaviours. Many such systems are embedded and used in safety-critical situations, to mention implantable medical devices. This thesis aims to develop a formal model-based framework that is tailored for the analysis and veri cation of cardiac pacemakers. The contributions are novel approaches for the automatic veri cation and validation of real-time properties over continuous-time models, which are applicable to software embedded in medical devices. First, we address the problem of model checking continuous-time Markov chain (CTMC) models against real-time speci cations given in the form of temporal logic, namely, metric temporal logic (MTL) and linear duration properties (LDP), or as timed automata (TA). The main question that we address is given a continuous-time Markov chain, what is the probability of the set of timed paths that satisfy the real-time property under consideration?". We provide novel algorithms to approximate the probability through generating systems of linear inequalities over variables that represent the waiting times in system states, and then solving multidimensional integrals over this set. Second, we present a model-based framework to support the design and veri cation of pacemakers against real-time properties. The pacemaker is modelled as a network of timed automata, whereas the human heart is modelled either as a network of timed automata or as a network of hybrid automata. Our framework can be instantiated with personalised heart models whose parameters can be learnt from patient data, and we have done so [LB13] to validate our approach. We introduce property patterns and the counting metric temporal logic (CMTL) in order to specify the properties of interest. We provide new veri cation algorithms for networks of timed or hybrid automata against property patterns and CMTL. Finally, we pose and solve the parameter synthesis problem, i.e., given a network of timed automata containing model parameters, an objective function and a CMTL formula, nd the set of parameter valuations, whenever existing, which satisfy the CMTL formula and maximise the objective function. The framework has been implemented using Simulink, Matlab and Python code. Extensive experimental results on pacemaker models have been carried out and discussed in detail. The techniques developed in this thesis can assist in the design and veri cation of software embedded in medical devices.