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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Alessandro Abate; Gilles Geeraerts. 15th International Conference on Formal Modelling and Analysis of Timed Systems (FORMATS), Sep 2017, Berlin, Germany. Lectures Notes in Computer Science (LNCS)
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Alexey Bakhirkin, Thomas Ferrère, Oded Maler, Dogan Ulus. On the Quantitative Semantics of Regular Expressions over Real-Valued Signals. Alessandro Abate; Gilles Geeraerts. 15th International Conference on Formal Modelling and Analysis of Timed Systems (FORMATS), Sep 2017, Berlin, Germany. Lectures Notes in Computer Science (LNCS). 〈hal-01552132〉

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