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== Timed language ==
The ''universal timed language'' <math>\Omega_{Z,[t_l, t_u]}</math> over an event set <math>Z</math> and a time interval <math>[t_l, t_u] \subset \mathbb{T}</math>, is denotedthe set of all event trajectories over <math>Z</math> and <math>[t_l,t_u]</math>. by
<math>\Omega_{Z,[t_l, t_u]}</math>, and is defined as the set of all possible event segments. Formally,
<center><math>
\Omega_{Z,[t_l,t_u]}=\{(z,t)^*| z \in Z \cup \{\epsilon\}, t \in [t_l, t_u] \}
</math> </center>
where <math>^*</math> denotes a none or multiple concatenation(s) of timed events. Notice that the number of events in an event segment <math>\omega \in
\Omega_{Z,[t_l, t_u]}</math> can be one of zero, finite or infinite.
Infinitely many events in an event segment <math>\omega \in \Omega_{Z,[t_l,
t_u]}</math> implies that <math>t_u - t_l \rightarrow \infty</math>, however <math>t_u - t_l \rightarrow
\infty</math> does not imply infinite many events in it.
A ''timed language'' <math>L</math> over an event set <math>Z</math> and a timed interval
<math>[t_l, t_u]</math> is ''a set of event segmentstrajectories'' over <math>Z</math> and <math>[t_l,
t_u]</math> if <math>L
t_u]</math>. If <math>L</math> is a language over <math>Z</math> and <math>[t_l, t_u]</math>, then <math>L
\subseteq \Omega_{Z, [t_l, t_u]}</math>.
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