  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 visualization and
testing applications.
