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Abstract. We present Montre, a monitoring tool to search patterns specified by timed regular expressions over real-time behaviors. We use timed regular expressions as a compact, natural, and highly-expressive pattern specification language for monitoring applications involving quantitative timing constraints. Our tool essentially incorporates online and offline timed pattern matching algorithms so it is capable of finding all occurrences of a given pattern over both logged and streaming behaviors. Furthermore, Montre is designed to work with other tools via standard interfaces to perform more complex and versatile tasks for analyzing and reasoning about cyber-physical systems. As the first of its kind, we believe Montre will enable a new line of inquiries and techniques in these fields.

Signal regular expressions can specify sequential properties of realvalued 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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Metric Temporal Logic (MTL) is a popular formalism to specify patterns with timing constraints over the behavior of cyber-physical systems. In this paper, I propose sequential networks for online monitoring applications and construct network-based monitors from the past fragment of MTL over discrete and dense time behaviors. This class of monitors is more compositional, extensible, and easily implementable than other monitors based on rewriting and automata. I first explain the sequential network construction over discrete time behaviors and then extend it towards dense time by adopting a point-free approach. The formulation for dense time behaviors and MTL radically differs from the traditional pointy definitions and, in return, we avoid some longstanding complications. I argue that the point-free approach is more natural and practical therefore should be preferred for the dense time. Finally, I present my implementation together with some experimental results that show the performance of the network-based monitors compared to similar existing tools.