Pattern Matching and Parameter Identification for Parametric Timed Regular Expressions.

Timed formalisms such as Timed Automata (TA), Signal Temporal Logic (STL) and Timed Regular expressions (TRE) have been previously applied as behaviour specifications for monitoring or runtime verification, in particular, under the form of pattern-matching, i.e. computing the set of all the segments of a given system run that satisfy the specification. In this work, timed regular expressions with parameters (for timing delays and for signal values) are considered. We define several classes of parametric expressions (based on Boolean or real-valued signals and discrete events), and tackle the problem of computing a parametric match-set, i.e. the parameter values and time segments of data that give a match for a given expression. We propose efficient data structures for representing match-sets (combining zones and polytopes), and devise pattern-matching algorithms. All these different types and algorithms are combined into a single implementation under a tool named parameTRE. We illustrate the approach on several examples, from electrocardiograms to driving patterns.