Online Quantitative Timed Pattern Matching with Semiring-Valued Weighted Automata

Abstract

Monitoring of a signal plays an essential role in the runtime verification of cyber-physical systems. Qualitative timed pattern matching is one of the mathematical formulations of monitoring, which gives a Boolean verdict for each sub-signal according to the satisfaction of the given specification. There are two orthogonal directions of extension of the qualitative timed pattern matching. One direction on the result is quantitative: what engineers want is often not a qualitative verdict but the quantitative measurement of the satisfaction of the specification. The other direction on the algorithm is online checking: the monitor returns some verdicts before obtaining the entire signal, which enables to monitor a running system. It is desired from application viewpoints. In this paper, we conduct these two extensions, taking an automata-based approach. This is the first quantitative and online timed pattern matching algorithm to the best of our knowledge. More specifically, we employ what we call timed symbolic weighted automata to specify quantitative specifications to be monitored, and we obtain an online algorithm using the shortest distance of a weighted variant of the zone graph and dynamic programming. Moreover, our problem setting is semiring-based and therefore, general. Our experimental results confirm the scalability of our algorithm for specifications with a time-bound.

Model-bounded monitoring of hybrid systems

“…In the context of quality assurance of CPSs, monitoring of digital (i. e., discrete-valued) or analog (i. e., continuous-valued) signals takes an important role. There have been many works on signal monitoring using various logic e. g., signal temporal logic (STL) [MN04; FP09], timed regular expressions (TREs) [Ulu+14], timed automata [Bak+18], or timed symbolic weighted automata (TSWAs) [Wag19]. However, in most of the existing works, interpolation of the sampled signals is limited to only piecewise-constant or piecewise-linear.…”

Symbolic Weighted Language Models, Quantitative Parsing and Automated Music Transcription

“…9], or nested words, with symbolic [7], or weighted [6] extensions of Visibly Pushdown Automata (VPA [2]). With their ability to evaluate data sequences quantitatively, sw models have found various applications such as data stream processing [3], runtime verification of timed systems [23] or robustness optimization for machine learning models [15].…”