On a simplified untiming procedure for supervisory control of timed automata when the time increases strictly monotonically

Given a timed automaton G accepting the timed language LT a finite state machine G' can be constructed, known as the region automaton, which accepts the untimed language Untime (LT). In this paper we construct an alternative finite state machine which also accepts the language Untime (LT), but has fewer states than G'. This is shown for languages of both finite and infinite traces given that the time values in the time sequence increase strictly monotonically. The supervisory control design for timed automata, when the simplified untiming procedure is used and the time is strictly positive, is studied.