The General System has been described in [Zeigler76] and [ZPK00] with the stand points to define (1) the time base, (2) the admissible input segments, (3) the system states, (4) the state trajectory with an admissible input segment, (5) the output for a given state.
A Timed Event System defining the state trajectory associated with the current and event segments is a sub-class of the class of General System. Since the behaviors of DEVS can be described by Timed Event System, DEVS is a sub-class or a equivalent class of Timed Event System.
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A timed event system is a structure
where
If is concatenation of two unit event segments, i.e., then
In general, if is concatenation of unit event segments, i.e., where then
Let and be two arbitrary sets. Then function is called deterministic if for , is identical any time. Otherwise, is called non-deterministic.
A Timed Event System is deterministic if
Otherwise, is non-deterministic.
Given a timed event system , the set of its behaviors is called its language depending on the observation time length. Let be the observation time length. If , -length observation language of is denoted by , and defined as
Notice that the reason why we need "there exists the case" is that we allow can be nondeterministic so the number of possible results can be many. Finally, we call an event segment a -length behavior of , if .
We can define behaviors with the infinite time length. Given an infinite-observation event segment and a timed event system , let denote the set of 's states that are infinitely many or long visited by and . Then infinite length observation language of is denoted by , and defined as
We call an event segment an infinite-length behavior of , if .