The Timestamp of Timed Automata

Abstract

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.

On the Distance Between Timed Automata

“…By [18], the timestamp of each of the events along γ A and γ B is an interval of the form (m, n), (m, n], [m, n) or [m, n], where m ≤ n and m ∈ N 0 , n ∈ N 0 ∪ {∞}. This can be shown by writing equalities and inequalities over the integers and variables z i , where z i represents the time of the i-th event along the path.…”

“…The augmented region automaton, denoted R t (A), is defined as in [18]. First, we add to A a clock t that measures absolute time, is never reset to 0 and does not affect the runs and timed traced of A. Secondly, we want to construct R t (A) in a way that keeps track of absolute time and regain much of the information that is lost when passing from the timed automaton A to the regular region automaton R(A).…”