Event segment

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