Place - Revision history

Vassia Atanassova at 21:18, 13 January 2011

2011-01-13T21:18:54Z

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 '''Places''' in the [[generalized nets]] are the second basic component of its static structure together with the [[transition]]s.
 == Types of GN places ==
 A place can play two roles with respect to a given transition:
 * input place for the transition,
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 The sets of input and output places of a given transition take part in the construction of its [[index matrix]] of predicates. The rows of the index matrix are labeled with the labels of the input places. The columns of the index matrix are labeled with the labels of the output places. The matrix element <math>{IP_i, OP_j}</math> that stays on the intersection of the <math>i</math>-th matrix row and <math>j</math>-th matrix column practically corresponds to the predicate that determines whether a token can pass from the <math>i</math>-th input place and <math>j</math>-th output place of the transition. When constructing the index matrix of a transition, it is important to take into consideration the eventual loops.
 : ''Example: Figure 3 represents the index matrix of transition <math>Z_1</math> from the simple generalized net, given on Figure 2. It is noteworthy that places <math>L_4</math> and <math>L_7</math> are input places for the transition <math>Z_1</math>. For the needs of the example, the values of the predicates have been randomly chosen; they do not follow from the graphical structure of the model, but rather from the logic of the modelled process.''

Vassia Atanassova at 20:41, 13 January 2011

2011-01-13T20:41:48Z

← Older revision		Revision as of 23:41, 13 January 2011
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	== Places and index matrices ==		== Places and index matrices ==
	The sets of input and output places of a given transition take part in the construction of its index matrix of predicates. The rows of the index matrix are labeled with the labels of the input places. The columns of the index matrix are labeled with the labels of the output places. The matrix element <math>{IP_i, OP_j}</math> that stays on the intersection of the <math>i</math>-th matrix row and <math>j</math>-th matrix column practically corresponds to the predicate that determines whether a token can pass from the <math>i</math>-th input place and <math>j</math>-th output place of the transition. When constructing the index matrix of a transition, it is important to take into consideration the eventual loops.		The sets of input and output places of a given transition take part in the construction of its [[index matrix]] of predicates. The rows of the index matrix are labeled with the labels of the input places. The columns of the index matrix are labeled with the labels of the output places. The matrix element <math>{IP_i, OP_j}</math> that stays on the intersection of the <math>i</math>-th matrix row and <math>j</math>-th matrix column practically corresponds to the predicate that determines whether a token can pass from the <math>i</math>-th input place and <math>j</math>-th output place of the transition. When constructing the index matrix of a transition, it is important to take into consideration the eventual loops.
	: ''Example: Figure 3 represents the index matrix of transition <math>Z_1</math> from the simple generalized net, given on Figure 2. It is noteworthy that places <math>L_4</math> and <math>L_7</math> are input places for the transition <math>Z_1</math>. For the needs of the example, the ~~current~~ values of the predicates ~~are~~ randomly chosen] they do not follow from the graphical structure of the model, but rather from the logic of the modelled process.''		: ''Example: Figure 3 represents the index matrix of transition <math>Z_1</math> from the simple generalized net, given on Figure 2. It is noteworthy that places <math>L_4</math> and <math>L_7</math> are input places for the transition <math>Z_1</math>. For the needs of the example, the values of the predicates have been randomly chosen; they do not follow from the graphical structure of the model, but rather from the logic of the modelled process.''

Vassia Atanassova: New page: '''Places''' in the generalized nets are the second basic component of its static structure together with the transitions. == Types of GN places == A place can play two roles wit...

2011-01-13T20:30:31Z

New page: '''Places''' in the generalized nets are the second basic component of its static structure together with the transitions. == Types of GN places == A place can play two roles wit...

New page

'''Places''' in the [[generalized nets]] are the second basic component of its static structure together with the [[transition]]s.

== Types of GN places ==
A place can play two roles with respect to a given transition:
* input place for the transition,
* output place for the transition.
: ''Example: On Figure 1, place <math>L_1</math> is input for transition <math>Z</math> and places <math>L_2, L_3</math> are outputs for this transition.''

A place that does not serve as a general input or output place for the whole generalized net, serves both as an output place for one transition and as an input place for another.
: ''Example: On Figure 2, the net's general inputs are places <math>L_1</math> and <math>L_5</math> and its general outputs are places <math>L_3</math> and <math>L_6</math>. Place <math>L_2</math> is output for transition <math>Z_1</math> and is input for transition <math>Z_2</math>.''
Some places are both input and output places for one transition; i.e. the tokens there can do loop.
: ''Example: On Figure 2, such places are <math>L_4</math> and <math>L_7</math>.''

== Places and index matrices ==
The sets of input and output places of a given transition take part in the construction of its index matrix of predicates. The rows of the index matrix are labeled with the labels of the input places. The columns of the index matrix are labeled with the labels of the output places. The matrix element <math>{IP_i, OP_j}</math> that stays on the intersection of the <math>i</math>-th matrix row and <math>j</math>-th matrix column practically corresponds to the predicate that determines whether a token can pass from the <math>i</math>-th input place and <math>j</math>-th output place of the transition. When constructing the index matrix of a transition, it is important to take into consideration the eventual loops.
: ''Example: Figure 3 represents the index matrix of transition <math>Z_1</math> from the simple generalized net, given on Figure 2. It is noteworthy that places <math>L_4</math> and <math>L_7</math> are input places for the transition <math>Z_1</math>. For the needs of the example, the current values of the predicates are randomly chosen] they do not follow from the graphical structure of the model, but rather from the logic of the modelled process.''