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

Behavior of DEVS

Behaviors of a given DEVS model is a set of sequences of timed events including null events, called event segments which make the model move one state to another within a set of legal states...

 can be described by Timed Event System, DEVS

DEVS

DEVS abbreviating Discrete Event System Specification is a modular and hierarchical formalism for modeling and analyzing general systems that can be discrete event systems which might be described by state transition tables, and continuous state systems which might be described by differential...

 is a sub-class or a equivalent class of Timed Event System.

Timed Event Systems

A timed event system is a structure

where

• is the set of events;
• is the set of states;
• is the initial state;
• is the set of acceptance states;
• is the state trajectory function that defines how a state changes into along with an event segment .
  
  If is concatenation of two unit event segments, i.e., then
  
  
  In general, if is concatenation of unit event segments, i.e., where then
  
  
  

  Deterministic System and Non-deterministic System

  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
  
  1. selecting is deterministic, and
  2. is deterministic.
  
  
  Otherwise, is non-deterministic.
  

  Behaviors and Languages of Timed Event System

  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 .
  The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.