@inproceedings{636,
  abstract     = {Signal regular expressions can specify sequential properties of real-valued signals based on threshold conditions, regular operations, and duration constraints. In this paper we endow them with a quantitative semantics which indicates how robustly a signal matches or does not match a given expression. First, we show that this semantics is a safe approximation of a distance between the signal and the language defined by the expression. Then, we consider the robust matching problem, that is, computing the quantitative semantics of every segment of a given signal relative to an expression. We present an algorithm that solves this problem for piecewise-constant and piecewise-linear signals and show that for such signals the robustness map is a piecewise-linear function. The availability of an indicator describing how robustly a signal segment matches some regular pattern provides a general framework for quantitative monitoring of cyber-physical systems.},
  author       = {Bakhirkin, Alexey and Ferrere, Thomas and Maler, Oded and Ulus, Dogan},
  editor       = {Abate, Alessandro and Geeraerts, Gilles},
  isbn         = {978-331965764-6},
  location     = {Berlin, Germany},
  pages        = {189 -- 206},
  publisher    = {Springer},
  title        = {{On the quantitative semantics of regular expressions over real-valued signals}},
  doi          = {10.1007/978-3-319-65765-3_11},
  volume       = {10419},
  year         = {2017},
}