 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. To define this way, the concept of a set of illegal state as well a set of legal states are needed to be introduced.
In addition, since the behaviors of a given DEVS model needs to define how the state transition change both when time is passed by and when an event occurs, it has been described by a much general formalism, called general system [ZPK00]. In this article, we use a subclass of General System formalism, called timed event system instead.
Depending on how to define the total state and its external state transition function of DEVS, two ways to define the behavior of a DEVS model using Timed Event System. Since behavior of a coupled DEVS model is defined as an atomic DEVS model, behavior of coupled DEVS class is defined by timed event system.
Contents
View 1: total states = states * elapsed times
Suppose that a DEVS model, has
 the total state set where t_{e} denotes elapsed time since last event and denotes the set of nonnegative real numbers, and
 the external state transition .
Then the DEVS model, is a Timed Event System where
 The event set .
 The state set .
 The initial state .
 The set of acceptance states
 The state trajectory function is defined for an total state at time and an event segment as follows.
If unit event segment ω is a timed event ω = (x,t) where the event is an input event ,
If unit event segment ω is a timed event ω = (y,t) where the event is an output event or the unobservable event ,
Computer algorithms to simulate this view of behavior are available at Simulation Algorithms for Atomic DEVS.
View 2: total states = states * lifespans * elapsed times
Suppose that a DEVS model, has
 the total state set where t_{s} denotes lifespan of state s, t_{e} denotes elapsed time since last t_{s}update, and denotes the set of nonnegative real numbers plus infinity,
 the external state transition is .
Then the DEVS is a timed event system where
 The event set .
 The state set .
 The initial state .
 The set of acceptance states .
 The state trajectory function is defined for a total state at time and an event segment as follows.
If unit event segment ω is a timed event ω = (x,t) where the event is an input event ,
If unit event segment ω is a timed event ω = (y,t) where the event is an output event or the unobservable event ,
Computer algorithms to simulate this view of behavior are available at Simulation Algorithms for Atomic DEVS.
Comparison of View1 and View2
Features of View1
View1 has been introduced by Zeigler [Zeigler84] in which given a total state and
where σ is the remaining time [Zeigler84] [ZPK00]. In other words, the set of partial states is indeed where S' is a state set.
When a DEVS model receives an input event , View1 resets the elapsed time t_{e} by zero, if the DEVS model needs to ignore x in terms of the lifepan control, modellers have to update the remaining time
in the external state transition function δ_{ext} that is the responsibility of the modellers.
Since the number of possible values of σ is the same as the number of possible input events coming to the DEVS model, that is unlimited. As a result, the number of states is also unlimited that is the reason why View2 has been proposed.
If we don't care the finitevertex reachability graph of a DEVS model, View1 has an advantage of simplicity for treating the elapsed time t_{e} = 0 every time any input event arrives into the DEVS model. But disadvantage might be modelers of DEVS should know how to manage σ as above, which is not explicitly explained in δ_{ext} itself but in Δ.
Features of View2
View2 has been introduced by Hwang and Zeigler[HZ06][HZ07] in which given a total state , the remaining time, σ is computed as
When a DEVS model receives an input event , View2 resets the elapsed time t_{e} by zero only if δ_{ext}(q,x) = (s',1). If the DEVS model needs to ignore x in terms of the lifepan control, modellers can use δ_{ext}(q,x) = (s',0).
Unlike View1, since the remaining time σ is not component of S in nature, if the number of states, i.e.  S  is finite, we can draw a finitevertex (as well as edge) statetransition diagram [HZ06][HZ07]. As a result, we can abstract behavior of such a DEVSclass network, for example SPDEVS and FDDEVS, as a finitevertex graph, called reachability graph [HZ06][HZ07].
See also
 Behavior of Coupled DEVS
 Simulation Algorithms for Atomic DEVS
 Simulation Algorithms for Coupled DEVS
References
 [Zeigler76] Bernard Zeigler (1976). Theory of Modeling and Simulation (first ed.). Wiley Interscience, New York.
 [Zeigler84] Bernard Zeigler (1984). Multifacetted Modeling and Discrete Event Simulation. Academic Press, London; Orlando. ISBN 9780127784502.
 [ZKP00] Bernard Zeigler, Tag Gon Kim, Herbert Praehofer (2000). Theory of Modeling and Simulation (second ed.). Academic Press, New York. ISBN 9780127784557.
 [HZ06] M. H. Hwang and B. P. Zeigler, ``A Reachable Graph of Finite and Deterministic DEVS Networks``, Proceedings of 2006 DEVS Symposium, pp4856, Huntsville, Alabama, USA, (Available at http://www.acims.arizona.edu and http://moonho.hwang.googlepages.com/publications)
 [HZ07] M.H. Hwang and B.P. Zeigler, ``Reachability Graph of Finite & Deterministic DEVS``, IEEE Transactions on Automation Science and Engineering, Volume 6, Issue 3, 2009, pp.454–467, http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?isnumber=5153598&arnumber=5071137&count=19&index=7
Categories: Automata theory
 Formal specification languages
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