Lost in Translation: Hybrid-Time Flows vs. Real-Time Transitions

Recently, hybrid-time flow systems have been introduced as an extension to timed transition systems, hybrid automata, continuous time evolutions of differential equations etc. Furthermore, a number of notions of bisimulation have been defined on these flow systems reflecting abstraction from certain timing properties. In this paper, we research the difference in abstraction level between this new semantic model of flow systems, and the more traditional model of real-time transition systems. We explore translations between the old and new semantic models, and we give a necessary and sufficient condition, called finite-set refutability, for these translations to be without loss of information. Finally, we show that differential inclusions with an upper-semicontinuous, closed and convex right-hand side, are finite-set refutable, and easily extend this result to impuls differential inclusions and hybrid automata.