A Uniform Framework for Timed Automata and Beyond

Timed automata, and machines alike, currently lack a general mathematical characterisation. This work introduces a uniform understanding of these devices that encompasses known behavioural equivalences such as timed bisimulations and timed language equivalences as well as their weak and time-abstract counterparts. All these notions of equivalence between systems are naturally organised in expressiveness spectra based on their discriminating power; these spectra are shown to be independent from any particular computational effect expressed by the systems under scrutiny. As an application, timed automata and their quantitative extensions such as probabilistic ones are studied.