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 $L \subseteq \Omega_{Z, }$ .

Read more about this topic: Event Segment

Famous quotes containing the words timed and/or language:

“Like most vigorous-minded men, seeing that there was no stopping-place between dogma and negation, he preferred to accept dogma. Of all weaknesses he most disliked timed and half-hearted faith. He would rather have jumped at once to Strong’s pure denial, than yield an inch to the argument that a mystery was to be paltered with because it could not be explained.”
—Henry Brooks Adams (1838–1918)

“The face of the water, in time, became a wonderful book—a book that was a dead language to the uneducated passenger, but which told its mind to me without reserve, delivering its most cherished secrets as clearly as if it uttered them with a voice. And it was not a book to be read once and thrown aside, for it had a new story to tell every day.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)