The Timestamp of Timed Automata

Given a member A of the class of non-deterministic timed automata with silent transitions (eNTA), we show how one can effectively compute its timestamp: the set of all pairs of time values and the corresponding actions of all observable timed traces of A, and also a deterministic timed automaton with the same timestamp as that of A. The timestamp is eventually periodic and is constructed via a finite periodic augmented region automaton. A consequence of this construction is the periodicity of the language of timed automata with respect to suffixes. Applications include the decidability of the 1-bounded language inclusion problem for the class eNTA, and a partial method, not bounded by time or number of steps, for the general language non-inclusion problem for eNTA.