At timed level of abstraction, system behaviors are considered as sequences of discrete events (from a finite alphabet) and real-valued time lapses between them; or as discrete-valued signals over continuous time. Initiated by works of Alur & Dill and aiming modeling and verification of real-time sequences, this approach became quite popular was successfully extended to other domains. As usual in verification, sets of timed behaviors were defined by (timed) automata, and by logical formulas.

In mid 90s, Oded Maler initiated a search for simpler, suitable for engineers, and still powerful formalism to describe sets of timed behaviors. After overcoming many technical obstacles, timed regular expressions were born, and their equivalence to timed automata proven. In follow-up works, alternative formalisms have been proposed by several researchers.

In 2010s, Oded Maler and his group came back to timed regular expressions, with a new optics of pattern-matching: given a (large) record of timed behavior of a system, and a timed regular expression describing patterns of interest (e.g. faulty sequences), detect all the occurrences of the pattern in the record. Most of this research is automata-free: pattern-matching algorithms work directly on timed behaviors. Efficient algorithms have been developed and implemented, allowing off-line and on-line pattern-matching, and using several formalisms for pattern specification, and applications to monitoring prospected.

In this talk I will present the timed view on system behaviors, and the two periods of timed regular expressions: theoretical study on expressiveness from 1990s and practice-oriented works on pattern-matching and monitoring from 2010s. No special knowledge is required from the audience. This will also be a memorial talk, on Oded’s philosophical, creative and personal style of choosing research topics, leading research, and supervising students and co-workers.