Event segment: Difference between revisions

Revision as of 13:47, 9 May 2012

Revision as of 04:18, 28 May 2012

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=== Unit event segment ===

A ''unit event segment'' is either a [[Event Segment#Null Eventevent Segmentsegment|null event segment]] or a [[Event Segment#Timed Eventevent|timed event]].

=== Concatenation ===

Given an event set <math>Z</math>, ''concatenation'' of two [[Event Segment#Unit Eventevent Segmentsegment|unit event segments]] <math>\omega</math> over <math>[t_1, t_2]</math> and <math>\omega'</math> over <math>[t_3,

t_4]</math> is denoted by <math>\omega\omega'</math> whose time interval is <math>[t_1,

t_4]</math>, and implies <math>t_2 = t_3</math>.

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=== Multi-event segment ===

A ''multi-event segment''

<math>(z_1,t_1)(z_2,t_2) \cdots (z_n,t_n)</math> over an event set <math> Z </math> and a time interval <math>[t_l, t_u] \subset \mathbb{T} </math> is concatenation of [[Event Segment#Unit Eventevent Segmentsegment|unit event segments]] <math>\epsilon_{[t_l,t_1]},(z_1,t_1), \epsilon_{[t_1,t_2]},(z_2,t_2),\ldots, (z_n,t_n),</math> and <math>\epsilon_{[t_n,t_u]}</math> where

<math>t_l\le t_1 \le t_2 \le \cdots \le t_{n-1} \le t_n \le t_u</math>.