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On the Quantitative Semantics of Regular Expressions over Real-Valued Signals

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.
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Submitted on : Friday, June 30, 2017 - 7:33:04 PM
Last modification on : Wednesday, November 3, 2021 - 4:29:56 AM
Long-term archiving on: : Monday, January 22, 2018 - 10:23:57 PM


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  • HAL Id : hal-01552132, version 1



Alexey Bakhirkin, Thomas Ferrère, Oded Maler, Dogan Ulus. On the Quantitative Semantics of Regular Expressions over Real-Valued Signals. 15th International Conference on Formal Modelling and Analysis of Timed Systems (FORMATS), Sep 2017, Berlin, Germany. ⟨hal-01552132⟩



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