conference paper published yes Alexey Bakhirkin author Thomas Ferrere author 40960E6E-F248-11E8-B48F-1D18A9856A870000-0001-5199-3143 Oded Maler author Dogan Ulus author AlessandroAbate editor GillesGeeraerts editor ToHe department FORMATS: Formal Modelling and Analysis of Timed Systems Moderne Concurrency Paradigms project Formal methods for the design and analysis of complex systems project 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. Springer2017Berlin, Germany eng 978-331965764-6 00061167830001110.1007/978-3-319-65765-3_11 10419189 - 206 Bakhirkin A, Ferrere T, Maler O, Ulus D. On the quantitative semantics of regular expressions over real-valued signals. In: Abate A, Geeraerts G, eds. Vol 10419. Springer; 2017:189-206. doi:<a href="https://doi.org/10.1007/978-3-319-65765-3_11">10.1007/978-3-319-65765-3_11</a> Bakhirkin, A., Ferrere, T., Maler, O., &#38; Ulus, D. (2017). On the quantitative semantics of regular expressions over real-valued signals. In A. Abate &#38; G. Geeraerts (Eds.) (Vol. 10419, pp. 189–206). Presented at the FORMATS: Formal Modelling and Analysis of Timed Systems, Berlin, Germany: Springer. <a href="https://doi.org/10.1007/978-3-319-65765-3_11">https://doi.org/10.1007/978-3-319-65765-3_11</a> A. Bakhirkin, T. Ferrere, O. Maler, and D. Ulus, “On the quantitative semantics of regular expressions over real-valued signals,” presented at the FORMATS: Formal Modelling and Analysis of Timed Systems, Berlin, Germany, 2017, vol. 10419, pp. 189–206. Bakhirkin, Alexey, et al. <i>On the Quantitative Semantics of Regular Expressions over Real-Valued Signals</i>. Edited by Alessandro Abate and Gilles Geeraerts, vol. 10419, Springer, 2017, pp. 189–206, doi:<a href="https://doi.org/10.1007/978-3-319-65765-3_11">10.1007/978-3-319-65765-3_11</a>. Bakhirkin A, Ferrere T, Maler O, Ulus D. 2017. On the quantitative semantics of regular expressions over real-valued signals. FORMATS: Formal Modelling and Analysis of Timed Systems, LNCS, vol. 10419, 189–206. A. Bakhirkin, T. Ferrere, O. Maler, D. Ulus, in:, A. Abate, G. Geeraerts (Eds.), Springer, 2017, pp. 189–206. Bakhirkin, Alexey, Thomas Ferrere, Oded Maler, and Dogan Ulus. “On the Quantitative Semantics of Regular Expressions over Real-Valued Signals.” edited by Alessandro Abate and Gilles Geeraerts, 10419:189–206. Springer, 2017. <a href="https://doi.org/10.1007/978-3-319-65765-3_11">https://doi.org/10.1007/978-3-319-65765-3_11</a>. 6362018-12-11T11:47:38Z2025-09-11T07:24:11Z