Event segment: Difference between revisions

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{{context|date=November 2011}}

A '''segment''' of a system variable 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 96km96&nbsp;km per hour for speed). Mathematically, a segment is a function mapping from a set of times which can be defined by an real interval, to the set <math>Z</math> [[Event_Segment#References|[Zeigler76]]],[[Event_Segment#References|[ZPK00]]], [[Event_Segment#References|[Hwang13]]]. 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 System]]s such as [[DEVS]], [[timed automaton|timed automata]], and [[timed petri nets]].

== Event segments ==

=== Time base ===

The ''time base'' of the concerning systems is denoted by <math> \mathbb{T} </math>, and defined

<center><math> \mathbb{T}=[0,\infty) </math> </center>

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<math>t_l\le t_1 \le t_2 \le \cdots \le t_{n-1} \le t_n \le t_u</math>.

Mathematically, an event trajectory is a mapping <math>\omega</math> a time period <math>[t_l,t_u] \subseteq \mathbb{T} </math> to an event set <math>Z</math>. So we can write it in a function form :

<center><math> \omega:[t_l,t_u] \rightarrow Z^* .</math></center>

== Timed language ==

The ''universal timed language'' <math>\Omega_{Z,[t_l, t_u]}</math> over an event set <math>Z</math> and a time interval <math>[t_l, t_u] \subset \mathbb{T}</math>, is the set of all event trajectories over <math>Z</math> and <math>[t_l,t_u]</math>.

A ''timed language'' <math>L</math> over an event set <math>Z</math> and a timed interval

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== References ==

* [Zeigler76] {{cite book|author = Bernard Zeigler | year = 1976| title = Theory of Modeling and Simulation| publisher = Wiley Interscience, New York | id = |edition=first}}

* [ZKP00] {{cite book|author author1= Bernard Zeigler, |author2=Tag Gon Kim, |author3=Herbert Praehofer | year = 2000| title = Theory of Modeling and Simulation| publisher = Academic Press, New York | isbn= 978-0-12-778455-7 |edition=second}}

* [Giambiasi01] Giambiasi N., Escude B. Ghosh S. “Generalized Discrete Event Simulation of Dynamic Systems”, in: Issue 4 of SCS Transactions: Recent Advances in DEVS Methodology-part II, Vol. 18, pp. 216-229&nbsp;216–229, dec 2001

* [Hwang13] M.H. Hwang, ``Revisit of system variable trajectories``, ''Proceedings of the Symposium on Theory of Modeling & Simulation - DEVS Integrative M&S Symposium '', San Diego, CA, USA, April 7 - 107–10, 2013

[[Category:Automata (computation)]]

[[Category:Formal specification languages]]