A simplification of the untiming procedure for timed automata defining languages of finite strings

Given an Alur Timed Automaton G accepting the language L
^T
, as defined in [1], a finite state machine G can be constructed, which accepts the language Untime(L
^T
). G is known as the region automaton. Here we construct an alternative finite state machine G ∗ that also accepts the language Untime(L
^T
), but has significantly fewer states than G. The new untiming procedure involves finite timed words only.