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Cyber-physical systems (CPS) are increasingly becoming driven by data, using multiple types of sensors to capture huge amounts of data. Extraction and characterization of useful information from big streams of data is a challenging problem. Shape expressions facilitate formal specification of rich temporal patterns encountered in time series as well as in behaviors of CPS. In this paper, we introduce a method for systematically sampling shape expressions. The proposed approach combines methods for uniform sampling of automata (for exploring qualitative shapes) with hit-and-run Monte Carlo sampling procedures (for exploring multi-dimensional parameter spaces defined by sets of possibly non-linear constraints). We study and implement several possible solutions and evaluate them in the context of visualisation and testing applications.

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