Event Segment - Timed Language

Timed Language

The universal timed language over an event set and a time interval, is denoted by, and is defined as the set of all possible event segments. Formally,

$\Omega_{Z,}=\{(z,t)^*| z \in Z \cup \{\epsilon\}, t \in \}$

where denotes a none or multiple concatenation(s) of timed events. Notice that the number of events in an event segment $\omega \in \Omega_{Z,}$ can be one of zero, finite or infinite. Infinitely many events in an event segment $\omega \in \Omega_{Z,[t_l, t_u]}$ implies that, however $t_u - t_l \rightarrow \infty$ does not imply infinite many events in it.

A timed language over an event set and a timed interval is a set of event segments over and $[t_l, t_u]$ . If is a language over and, then $L \subseteq \Omega_{Z, }$ .

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