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The rise of machine learning and cloud technologies has led to a remarkable influx of data within modern cyber-physical systems. However, extracting meaningful information from this data has become a significant challenge due to its volume and complexity. Timed pattern matching has emerged as a powerful specification-based runtime verification and temporal data analysis technique to address this challenge. In this paper, we provide a comprehensive tutorial on timed pattern matching that ranges from the underlying algebra and pattern specification languages to performance analyses and practical case studies. Analogous to textual pattern matching, timed pattern matching is the task of finding all time periods within temporal behaviors of cyber-physical systems that match a predefined pattern. Originally we introduced and solved several variants of the problem using the name of match sets, which has evolved into the concept of timed relations over the past decade. Here we first formalize and present the algebra of timed relations as a standalone mathematical tool to solve the pattern matching problem of timed pattern specifications. In particular, we show how to use the algebra of timed relations to solve the pattern matching problem for timed regular expressions and metric compass logic in a unified manner. We experimentally demonstrate that our timed pattern matching approach performs and scales well in practice. We further provide in-depth insights into the similarities and fundamental differences between monitoring and matching problems as well as regular expressions and temporal logic formulas. Finally, we illustrate the practical application of timed pattern matching through two case studies, which show how to extract structured information from temporal datasets obtained via simulations or real-world observations. These results and examples show that timed pattern matching is a rigorous and efficient technique in developing and analyzing cyber-physical systems. [ABSTRACT FROM AUTHOR]

Shape expressions (SEs) is a novel specification language that was recently introduced to express behavioral patterns over real-valued signals observed during the execution of cyber-physical systems. An SE is a regular expression composed of arbitrary parameterized shapes, such as lines, exponential curves, and sinusoids as atomic symbols with symbolic constraints on the shape parameters. SEs enable a natural and intuitive specification of complex temporal patterns over possibly noisy data. In this article, we propose a novel method for mining a broad and interesting fragment of SEs from time-series data using a combination of techniques from linear regression, unsupervised clustering, and learning finite automata from positive examples. The learned SE for a given dataset provides an explainable and intuitive model of the observed system behavior. We demonstrate the applicability of our approach on two case studies from different application domains and experimentally evaluate the implemented specification mining procedure. [ABSTRACT FROM AUTHOR]

Runtime verification (RV) is a pragmatic and scalable, yet rigorous technique, to assess the correctness of complex systems, including cyber-physical systems (CPSs). Modern RV tools also allow to measure the distance of a CPS behavior from a given formal requirement, thus, to quantify the robustness of a CPS with respect to perturbations caused by the physical environment. In this paper, we propose algebraic RV (ARV), a general, semantic framework for correctness and robustness monitoring. ARV implements an abstract monitoring procedure, in which the specification language (STL) can be instantiated with various qualitative and quantitative semantics. This allows us to expose the core aspects of RV, by separating the monitoring algorithm from the concrete choice of the STL and its semantics. We demonstrate the effectiveness of our framework on two examples from the automotive domain. [ABSTRACT FROM AUTHOR]