Algorithm for generalized net functioning - Revision history

Peter Vassilev at 14:26, 1 June 2015

2015-06-01T14:26:26Z

← Older revision		Revision as of 17:26, 1 June 2015
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	where:		where:
	* ~~{{#tag:~~math\| f(r_{i,j})= \begin{cases} 1 & if \ the \ predicate \ r_{i,j} \ is ~~\ "~~true" \\ 0 & otherwise \end{cases} }}		* <math>f(r_{i,j})= \begin{cases}1 \text{ if the predicate } r_{i,j} \text{ is ``true'' } \\ 0 \text{ otherwise } \end{cases} </math>
	* <math>m_{i,j}</math> is the capacity of this arc, which decrements with 1 for each token that passes during the transfer at the current moment <math>TIME</math>. When it reaches zero, the arc capacity will be fully utilized and no more tokens may pass at this time.		* <math>m_{i,j}</math> is the capacity of this arc, which decrements with 1 for each token that passes during the transfer at the current moment <math>TIME</math>. When it reaches zero, the arc capacity will be fully utilized and no more tokens may pass at this time.
	* <math>\overline{c}(l_i, TIME)</math> is the number of tokens, which at moment <nowiki>TIME</nowiki> stay in the input place <math>l_i</math>. When there are no tokens in the input place, no transfer may occur and the process will stop.		* <math>\overline{c}(l_i, TIME)</math> is the number of tokens, which at moment <nowiki>TIME</nowiki> stay in the input place <math>l_i</math>. When there are no tokens in the input place, no transfer may occur and the process will stop.

Peter Vassilev: /* Conclusions */

2015-05-26T14:25:27Z

Conclusions

← Older revision		Revision as of 17:25, 26 May 2015
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	where:		where:
	* {{#tag:math\| f(r_{i,j})= {{\begin{cases}		* {{#tag:math\| f(r_{i,j})= \begin{cases} 1 & if \ the \ predicate \ r_{i,j} \ is \ "true" \\ 0 & otherwise \end{cases} }}
	1 & if \ the \ predicate \ r_{i,j} \ is \ "true" \\
	0 & otherwise
	\end{cases~~} }~~} }}
	* <math>m_{i,j}</math> is the capacity of this arc, which decrements with 1 for each token that passes during the transfer at the current moment <math>TIME</math>. When it reaches zero, the arc capacity will be fully utilized and no more tokens may pass at this time.		* <math>m_{i,j}</math> is the capacity of this arc, which decrements with 1 for each token that passes during the transfer at the current moment <math>TIME</math>. When it reaches zero, the arc capacity will be fully utilized and no more tokens may pass at this time.
	* <math>\overline{c}(l_i, TIME)</math> is the number of tokens, which at moment <nowiki>TIME</nowiki> stay in the input place <math>l_i</math>. When there are no tokens in the input place, no transfer may occur and the process will stop.		* <math>\overline{c}(l_i, TIME)</math> is the number of tokens, which at moment <nowiki>TIME</nowiki> stay in the input place <math>l_i</math>. When there are no tokens in the input place, no transfer may occur and the process will stop.

Peter Vassilev: /* Conclusions */

2015-05-26T14:21:09Z

Conclusions

← Older revision		Revision as of 17:21, 26 May 2015
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	where:		where:
	* {{#tag:math\| f(r_{i,j})= \begin{cases}		* {{#tag:math\| f(r_{i,j})= {{\begin{cases}
	1 & if \ the \ predicate \ r_{i,j} \ is \ "true" \\		1 & if \ the \ predicate \ r_{i,j} \ is \ "true" \\
	0 & otherwise		0 & otherwise
	\end{cases} }}		\end{cases} }} }}
	* <math>m_{i,j}</math> is the capacity of this arc, which decrements with 1 for each token that passes during the transfer at the current moment <math>TIME</math>. When it reaches zero, the arc capacity will be fully utilized and no more tokens may pass at this time.		* <math>m_{i,j}</math> is the capacity of this arc, which decrements with 1 for each token that passes during the transfer at the current moment <math>TIME</math>. When it reaches zero, the arc capacity will be fully utilized and no more tokens may pass at this time.
	* <math>\overline{c}(l_i, TIME)</math> is the number of tokens, which at moment <nowiki>TIME</nowiki> stay in the input place <math>l_i</math>. When there are no tokens in the input place, no transfer may occur and the process will stop.		* <math>\overline{c}(l_i, TIME)</math> is the number of tokens, which at moment <nowiki>TIME</nowiki> stay in the input place <math>l_i</math>. When there are no tokens in the input place, no transfer may occur and the process will stop.

Peter Vassilev: /* Conclusions */

2015-05-26T14:19:35Z

Conclusions

← Older revision		Revision as of 17:19, 26 May 2015
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	where:		where:
	* {{#tag:math\| f(r_{i,j})= \begin{cases}		* {{#tag:math\| f(r_{i,j})= \begin{cases}
	1 if \ the \ predicate \ r_{i,j} \ is \ "true" \\		1 & if \ the \ predicate \ r_{i,j} \ is \ "true" \\
	0 otherwise		0 & otherwise
	\end{cases} }}		\end{cases} }}
	* <math>m_{i,j}</math> is the capacity of this arc, which decrements with 1 for each token that passes during the transfer at the current moment <math>TIME</math>. When it reaches zero, the arc capacity will be fully utilized and no more tokens may pass at this time.		* <math>m_{i,j}</math> is the capacity of this arc, which decrements with 1 for each token that passes during the transfer at the current moment <math>TIME</math>. When it reaches zero, the arc capacity will be fully utilized and no more tokens may pass at this time.

Peter Vassilev: /* Conclusions */

2015-05-26T14:18:51Z

Conclusions

← Older revision		Revision as of 17:18, 26 May 2015
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	where:		where:
	* {{#tag:math\| f(r_{i,j})= \begin{cases}		* {{#tag:math\| f(r_{i,j})= \begin{cases}
	1 & if \ the \ predicate \ r_{i,j} \ is \ "true" \\		1 if \ the \ predicate \ r_{i,j} \ is \ "true" \\
	0 & otherwise		0 otherwise
	\end{cases} }}		\end{cases} }}
	* <math>m_{i,j}</math> is the capacity of this arc, which decrements with 1 for each token that passes during the transfer at the current moment <math>TIME</math>. When it reaches zero, the arc capacity will be fully utilized and no more tokens may pass at this time.		* <math>m_{i,j}</math> is the capacity of this arc, which decrements with 1 for each token that passes during the transfer at the current moment <math>TIME</math>. When it reaches zero, the arc capacity will be fully utilized and no more tokens may pass at this time.

Peter Vassilev: /* Conclusions */

2015-05-26T14:11:12Z

Conclusions

← Older revision		Revision as of 17:11, 26 May 2015
Line 58:		Line 58:

	where:		where:
	* {{#tag:math\|f(r_{i,j})= \begin{cases}		* {{#tag:math\| f(r_{i,j})= \begin{cases}
	1 & if \ the \ predicate \ r_{i,j} \ is \ "true" \\		1 & if \ the \ predicate \ r_{i,j} \ is \ "true" \\
	0 & otherwise		0 & otherwise

Peter Vassilev: /* Conclusions */

2015-05-26T14:09:13Z

Conclusions

← Older revision		Revision as of 17:09, 26 May 2015
Line 58:		Line 58:

	where:		where:
	* <math>f(r_{i,j})= \begin{cases}		* {{#tag:math\|f(r_{i,j})= \begin{cases}
	1 & if \ the \ predicate \ r_{i,j} \ is \ "true" \\		1 & if \ the \ predicate \ r_{i,j} \ is \ "true" \\
	0 & otherwise		0 & otherwise
	\end{cases} ~~</math>~~		\end{cases} }}
	* <math>m_{i,j}</math> is the capacity of this arc, which decrements with 1 for each token that passes during the transfer at the current moment <math>TIME</math>. When it reaches zero, the arc capacity will be fully utilized and no more tokens may pass at this time.		* <math>m_{i,j}</math> is the capacity of this arc, which decrements with 1 for each token that passes during the transfer at the current moment <math>TIME</math>. When it reaches zero, the arc capacity will be fully utilized and no more tokens may pass at this time.
	* <math>\overline{c}(l_i, TIME)</math> is the number of tokens, which at moment <nowiki>TIME</nowiki> stay in the input place <math>l_i</math>. When there are no tokens in the input place, no transfer may occur and the process will stop.		* <math>\overline{c}(l_i, TIME)</math> is the number of tokens, which at moment <nowiki>TIME</nowiki> stay in the input place <math>l_i</math>. When there are no tokens in the input place, no transfer may occur and the process will stop.

Vassia Atanassova at 21:11, 24 February 2014

2014-02-24T21:11:27Z

← Older revision		Revision as of 00:11, 25 February 2014
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	Below we will describe the most general algorithm for the [[generalized net]] functioning.		Below we will describe the most general algorithm for the [[generalized net]] functioning.

	For this purpose, we will introduce the concept of ''Abstract Transition'' (AT). This is a GN [[~~tranition~~]] represented as the union of all active GN-transitions at a given time-moment. For its construction the operation "union" of transitions is used (see [[Operations and relations over generalized nets]]).		For this purpose, we will introduce the concept of ''Abstract Transition'' (AT). This is a GN [[transition]] represented as the union of all active GN-transitions at a given time-moment. For its construction the operation "union" of transitions is used (see [[Operations and relations over generalized nets]]).

	== The algorithm ==		== The algorithm ==
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	\| style="padding-bottom:1em" \| Put all tokens ''α'', for which ''θ<sub>K</sub>(α) ≤ T'', into the corresponding input [[place]]s of the net.		\| style="padding-bottom:1em" \| Put all tokens ''α'', for which ''θ<sub>K</sub>(α) ≤ T'', into the corresponding input [[place]]s of the net.
	\|-valign="top"		\|-valign="top"
	\| '''Step B02'''		\| '''Step B02'''
	\| style="padding-bottom:1em" \| Construct the GN's Abstract Transition (initially it is empty).		\| style="padding-bottom:1em" \| Construct the GN's Abstract Transition (initially it is empty).
	\|-valign="top"		\|-valign="top"

Vassia Atanassova at 11:20, 23 November 2009

2009-11-23T11:20:41Z

@@ Line 3: / Line 3: @@
 For this purpose, we will introduce the concept of ''Abstract Transition'' (AT). This is a GN [[tranition]] represented as the union of all active GN-transitions at a given time-moment. For its construction the operation "union" of transitions is used (see [[Operations and relations over generalized nets]]).
 {| width="100%"
 |-valign="top"
@@ Line 46: / Line 47: @@
 This algorithm was described in the "[[Generalized Nets (World Scientific)|Generalized Nets]]" from 1991 year <ref>Atanassov K., "Generalized Nets", World Scientific, Singapore, 1991, ISBN 978-981-02-0598-0</ref> and "[[On Generalized Nets Theory]]" from 2007 year <ref>Atanassov K., [[On Generalized Nets Theory]], "Professor Marin Drinov" Academic Publishing House, 2007, ISBN 978-954-322-237-7</ref>.
 == References ==

Vassia Atanassova: New page: Below we will describe the most general algorithm for the generalized net functioning. For this purpose, we will introduce the concept of ''Abstract Transition'' (AT). This is a GN ...

2009-11-22T17:39:52Z

New page: Below we will describe the most general algorithm for the generalized net functioning. For this purpose, we will introduce the concept of ''Abstract Transition'' (AT). This is a GN ...

New page

Below we will describe the most general algorithm for the [[generalized net]] functioning.

For this purpose, we will introduce the concept of ''Abstract Transition'' (AT). This is a GN [[tranition]] represented as the union of all active GN-transitions at a given time-moment. For its construction the operation "union" of transitions is used (see [[Operations and relations over generalized nets]]).

{| width="100%"
|-valign="top"
| width="10%" | '''Step B01'''
| style="padding-bottom:1em" | Put all tokens ''α'', for which ''θ<sub>K</sub>(α) ≤ T'', into the corresponding input [[place]]s of the net.
|-valign="top"
| '''Step B02'''
| style="padding-bottom:1em" | Construct the GN's Abstract Transition (initially it is empty).
|-valign="top"
| '''Step B03'''
| style="padding-bottom:1em" | Check whether the value of the current time is less than ''T + t*''.
|-valign="top"
| '''Step B04'''
| style="padding-bottom:1em" | If the answer to the question on '''Step B03''' is "no", terminate the process of GN functioning.
|-valign="top"
| '''Step B05'''
| style="padding-bottom:1em" | Check all transitions for which the first time-component is exactly equal to the current time-moment.
|-valign="top"
| '''Step B06'''
| style="padding-bottom:1em" | Check the transition's types of all transitions determined by B05. The method of checking is as follows:
* Change the names of all places which participate in the Boolean expression of the [[transition type]] as variables with values:
** 0, if the corresponding place has no tokens at the current moment;
** 1, otherwise;
* Calculate the truth value of the so obtained Boolean expression.
|-valign="top"
| '''Step B07'''
| style="padding-bottom:1em" | Add all transitions from '''Step B06''', for which the transition types are satisfied by the Abstract Transition.
|-valign="top"
| '''Step B08'''
| style="padding-bottom:1em" | Apply the [[algorithm for transition functioning]] over the Abstract Transition.
|-valign="top"
| '''Step B09'''
| style="padding-bottom:1em" | Remove from the Abstract Transition all transitions, which are inactive at the current time-moment.
|-valign="top"
| '''Step B10'''
| style="padding-bottom:1em" | Increase the current time with ''t<sup>0</sup>''.
|-valign="top"
| '''Step B11'''
| style="padding-bottom:1em" | Go to '''Step B03'''.
|}

This algorithm helps us to realize the different subprocesses (which exist in the frames of the most global modelled process) on the level of places, while analogous processes in other nets are modelled on the level of transitions. Moreover, the places are sorted by their priorities while in other nets this is not the case. Therefore, the sequence of the process realization by generalized nets is performed on the level of places (from different active transitions). Furthermore, when some places have equal priority, the tokens' transfer is related to the tokens' priorities, which is difficult to achieve in other nets.

This algorithm was described in the "[[Generalized Nets (World Scientific)|Generalized Nets]]" from 1991 year <ref>Atanassov K., "Generalized Nets", World Scientific, Singapore, 1991, ISBN 978-981-02-0598-0</ref> and "[[On Generalized Nets Theory]]" from 2007 year <ref>Atanassov K., [[On Generalized Nets Theory]], "Professor Marin Drinov" Academic Publishing House, 2007, ISBN 978-954-322-237-7</ref>.

== References ==
<references />

[[Category:Generalized nets]]