Petri ağı: Revizyonlar arasındaki fark
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55. satır:
* <math>(S,T,W)</math> bir petri ağıdır.
* <math>M_0</math> (Petri ağına ait bir işaretleme olan) ''ilk işaretleme''dir.
=== Çalışma mantığı ===
In words:
* firing a transition ''t'' in a marking ''M'' consumes <math>W(s,t)</math> tokens from each of its input places ''s'', and produces <math>W(t,s)</math> tokens in each of its output places ''s''
* a transition is ''enabled'' (it may ''fire'') in ''M'' if there are enough tokens in its input places for the consumptions to be possible, i.e. iff <math>\forall s: M(s) \geq W(s,t)</math>.
We are generally interested in what may happen when transitions may continually fire in arbitrary order.
We say that a marking <math>M'</math> ''is reachable from'' a marking ''M'' ''in one step'' if <math>M \to_G M'</math>; we say that it ''is reachable from'' ''M'' if <math>M {\to_G}^* M'</math>, where <math>{\to_G}^*</math> is the [[reflexive transitive closure]] of <math>\to_G</math>; that is, if it is reachable in 0 or more steps.
For a (marked) Petri net <math>N=(S,T,W,M_0)\!</math>, we are interested in the firings that can be performed starting with the initial marking <math>M_0</math>. Its set of ''reachable markings'' is the set
<math>R(N) \ \stackrel{D}{=}\ \{ M' \mid M_0 {\to_{(S,T,W)}}^* M' \} </math>
The ''reachability graph'' of ''N'' is the transition relation <math>\to_G</math> restricted to its reachable markings <math>R(N)</math>. It is the [[state space]] of the net.
A ''firing sequence'' for a Petri net with graph ''G'' and initial marking <math>M_0</math> is a sequence of transitions <math>\vec \sigma = \langle t_{i_1} \ldots t_{i_n} \rangle</math> such that <math>M_0 \to_{G,t_{i_1}} M_1 \wedge \ldots \wedge M_{n-1} \to_{G,t_{i_n}} M_n</math>. The set of firing sequences is denoted as <math>L(N)</math>.
== References ==
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