On the quantitative semantics of regular expressions over real-valued signals

A. Bakhirkin, T. Ferrere, O. Maler, D. Ulus, in:, A. Abate, G. Geeraerts (Eds.), Springer, 2017, pp. 189–206.


Conference Paper | Published | English
Author
; ; ;
Editor
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Department
Series Title
LNCS
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.
Publishing Year
Date Published
2017-08-03
Volume
10419
Page
189 - 206
Conference
FORMATS: Formal Modelling and Analysis of Timed Systems
Conference Location
Berlin, Germany
Conference Date
2017-09-05 – 2017-09-07
IST-REx-ID

Cite this

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:10.1007/978-3-319-65765-3_11
Bakhirkin, A., Ferrere, T., Maler, O., & Ulus, D. (2017). On the quantitative semantics of regular expressions over real-valued signals. In A. Abate & G. Geeraerts (Eds.) (Vol. 10419, pp. 189–206). Presented at the FORMATS: Formal Modelling and Analysis of Timed Systems, Berlin, Germany: Springer. https://doi.org/10.1007/978-3-319-65765-3_11
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. https://doi.org/10.1007/978-3-319-65765-3_11.
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 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.
Bakhirkin, Alexey, et al. On the Quantitative Semantics of Regular Expressions over Real-Valued Signals. Edited by Alessandro Abate and Gilles Geeraerts, vol. 10419, Springer, 2017, pp. 189–206, doi:10.1007/978-3-319-65765-3_11.

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