A segment of a system variable in computing shows a homogenous status of system dynamics over a time period.
Here, a homogenous status of a variable is a state which can be described by a set of coefficients of a formula.
For example, of homogenous statuses, we can bring status of constant ('ON' of a switch) and linear (60 miles or 96 km per hour for speed).
Mathematically, a segment is a function mapping from a set of times which can be defined by a real interval, to the set
A trajectory of a system variable is a sequence of segments concatenated.
We call a trajectory constant (respectively linear) if its concatenating segments are constant (respectively linear).
An event segment is a special class of the constant segment with a constraint in which the constant segment is either one of a timed event or a null-segment.
The event segments are used to define Timed Event Systems such as DEVS, timed automata, and timed petri nets.
The time base of the concerning systems is denoted by
, and defined as the set of non-negative real numbers.
An event is a label that abstracts a change.
, the null event denoted by
A timed event is a pair
denotes that an event
occurs at time
The null segment over time interval
A unit event segment is either a null event segment or a timed event.
, concatenation of two unit event segments
whose time interval is
An event trajectory
and a time interval
is concatenation of unit event segments
Mathematically, an event trajectory is a mapping
a time period
So we can write it in a function form : The universal timed language
and a time interval
, is the set of all event trajectories over
A timed language
and a timed interval
is a set of event trajectories over