Specifying Timed Pa erns using Temporal Logic

Monitoring system behaviors using formal speci cations appears to be an e ective technique in analyzing cyber-physical systems. However, to achieve intended results in monitoring, speci cation languages need to be intuitive, elegant, and expressive at the rst place. In this paper, we propose a metric extension of well-known Halpern-Shoham (hs) logic, called Metric Compass Logic (mcl), for monitoring purposes. Originally proposed for high-level temporal reasoning, the logic hs is very expressive and enables users to specify many temporal patterns in an intuitive and elegant way. As our main contribution, we present an o ine monitoring technique for timed patterns speci ed inmcl. Our solution is built upon the framework developed for timed regular expressions (tre) matching but explores a di erent (logical) direction. We nally study several practical features concerning atomic formulas and discuss a combined timed pattern speci cation language with tre.