Online Quantitative Timed Pattern Matching with Semiring-Valued Weighted Automata

TL;DR

This paper introduces the first online, quantitative timed pattern matching algorithm using semiring-valued weighted automata, enabling real-time monitoring with quantitative satisfaction measures in cyber-physical systems.

Contribution

It presents a novel automata-based approach that combines online checking and quantitative analysis for timed pattern matching, extending prior qualitative methods.

Findings

Algorithm is scalable for time-bound specifications

Uses shortest distance in weighted zone graph for online computation

Employs semiring structure for generality

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.