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Two polygraphic presentations of Petri nets

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Title: Two polygraphic presentations of Petri nets
Authors: Guiraud, Yves1 guiraud@iml.univ-mrs.fr
Source: Theoretical Computer Science. Aug2006, Vol. 360 Issue 1-3, p124-146. 23p.
Subjects: Petri nets, Polygraph operators, Commutative algebra, Graph theory
Abstract: Abstract: This document gives an algebraic and two polygraphic translations of Petri nets, all three providing an easier way to describe reductions and to identify some of them. The first one sees places as generators of a commutative monoid and transitions as rewriting rules on it: this setting is totally equivalent to Petri nets, but lacks any graphical intuition. The second one considers places as one-dimensional cells and transitions as two-dimensional ones: this translation recovers a graphical meaning but raises many difficulties since it uses explicit permutations. Finally, the third translation sees places as degenerated two-dimensional cells and transitions as three-dimensional ones: this is a setting equivalent to Petri nets, equipped with a graphical interpretation. [Copyright &y& Elsevier]
Copyright of Theoretical Computer Science is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 21830351
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PubType: Academic Journal
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  Data: Two polygraphic presentations of Petri nets
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  Data: Abstract: This document gives an algebraic and two polygraphic translations of Petri nets, all three providing an easier way to describe reductions and to identify some of them. The first one sees places as generators of a commutative monoid and transitions as rewriting rules on it: this setting is totally equivalent to Petri nets, but lacks any graphical intuition. The second one considers places as one-dimensional cells and transitions as two-dimensional ones: this translation recovers a graphical meaning but raises many difficulties since it uses explicit permutations. Finally, the third translation sees places as degenerated two-dimensional cells and transitions as three-dimensional ones: this is a setting equivalent to Petri nets, equipped with a graphical interpretation. [Copyright &y& Elsevier]
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  Data: <i>Copyright of Theoretical Computer Science is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.tcs.2006.02.015
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      – SubjectFull: Commutative algebra
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