Mathematics – Category Theory
Scientific paper
2006-12-04
Theoretical Computer Science, Volume 360, Issues 1-3, 21 August 2006, Pages 124-146
Mathematics
Category Theory
28 pages, 24 figures
Scientific paper
10.1016/j.tcs.2006.02.015
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 1-dimensional cells and transitions as 2-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 2-dimensional cells and transitions as 3-dimensional ones: this is a setting equivalent to Petri nets, equipped with a graphical interpretation.
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