Timed and register automata are well-known models of computation over timed and data words, respectively. The former has clocks that allow to test the lapse of time between two events, whilst the latter includes registers that can store data values for later comparison. Although these two models behave differently in appearance, several decision problems have the same (un)decidability and complexity results for both models. As a prominent example, emptiness is decidable for alternating automata with one clock or register, both with non-primitive recursive complexity. This is not by chance.
This work confirms that there is indeed a tight relationship between the two models. We show that a run of a timed automaton can be simulated by a register automaton over ordered data domain, and conversely that a run of a register automaton can be simulated by a timed automaton. These are exponential time reductions hold both in the finite and infinite words settings. Our results allow to transfer decidability results back and forth between these two kinds of models, as well complexity results modulo an exponential time reduction. We justify the usefulness of these reductions by obtaining new results on register automata.