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Petri net: различия между версиями

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'''Petri net''' --- сеть Петри.  
'''Petri net''' ---''[[сеть Петри]]''.  


A ''' Petri net''' is a finite  directed graph with two types of nodes,
A ''' Petri net''' is a finite  directed graph with two types of nodes,
referred to as '''places''' and '''transitions'''. It is a bipartite graph: every arc
referred to as '''places''' and '''transitions'''. It is a bipartite graph: every arc
goes either from a place to a transition or from a transition to a place.
goes either from a place to a transition or from a transition to a place.
Consider a transition <math>t</math>. Every place <math>p</math> (respectively, <math>q</math>) such that there is an arc from <math>t</math> to <math>p</math>
Consider a transition <math>t</math>. Every place <math>p</math> (respectively, <math>q</math>) such that there is an arc from <math>t</math> to <math>p</math>
(respectively, from <math>q</math> to <math>t</math>) is called an '''input'''
(respectively, from <math>q</math> to <math>t</math>) is called an '''input'''
(respectivelyб an '''output''') '''place''' of <math>t</math>.
(respectively, an '''output''') '''place''' of <math>t</math>.
The same place can be both an input and an output place of <math>t</math>.
The same place can be both an input and an output place of <math>t</math>.


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Thus, formally, a (marked) Petri net is a quadruple <math>N=(P,T,A,m_0)</math>, where <math>P</math> and <math>T</math> are nonempty
Thus, formally, a (marked) Petri net is a quadruple <math>N=(P,T,A,m_0)</math>, where <math>P</math> and <math>T</math> are nonempty
finite disjoint sets of places and transi\-tions, <math>A</math> is a subset of <math>P \times T \bigcup T\times P</math>.
finite disjoint sets of places and transitions, <math>A</math> is a subset of <math>P \times T \bigcup T\times P</math>.
(It is often also required that the union of the domain and codomain of <math>A</math> equals <math>P\bigcup T</math>; that is,
(It is often also required that the union of the domain and codomain of <math>A</math> equals <math>P\bigcup T</math>; that is,
every place and transition is either the beginning or the end of some arc.) Finally, <math>m_0</math> (initial marking)
every place and transition is either the beginning or the end of some arc.) Finally, <math>m_0</math> (initial marking)
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We now define the '''operation''' (or '''execution''') of a Petri net.
We now define the '''operation''' (or '''execution''') of a Petri net.
A transition is '''enabled''' (at a marking) iff all its input places have at least one token.
A transition is '''enabled''' (at a marking) iff all its input places have at least one token.
An enabled transi\-tion may '''fire''' by removing one token from each of its input places and
An enabled transition may '''fire''' by removing one token from each of its input places and
adding one token to each of its output places.
adding one token to each of its output places.


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A transition is not enabled if there are not sufficiently many tokens in each
A transition is not enabled if there are not sufficiently many tokens in each
of its input places.
of its input places.
[[Категория:Теория вычислений]]