Higher-dimensional word problems with applications to equational logic
Selected papers of the 4th summer conference on Category theory and computer science
Term rewriting and all that
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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 diffficulties 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.