  In this work, we show that the model of timed discrete-event systems (TDES)
proposed by Brandin and Wonham is essentially a synchronous product structure.
This resolves an open problem that has remained unaddressed for the past 25
years and has its application in developing a more efficient timed state-tree
structures (TSTS) framework. The proof is constructive in the sense that an
explicit synchronous production rule is provided to generate a TDES from the
activity automaton and the timer automata after a suitable transformation of
the model.
