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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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)

“This is an approach to that universal language which men have sought in vain.”
—Henry David Thoreau (1817–1862)