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 expre...

We introduce a new formalism called automata over a timed domain which provides an adequate framework for the determinization of timed systems. In this formalism, determinization w.r.t. timed language is always possible at the cost of changing the timed domain. We give a condition for determinizability of automata over a timed domain without changing the timed domain, which allows us to recover...