Semi-Commutation and Deterministic Petri Nets

Semi-commutation rewriting systems have been introduced and investigated by Clerbout/Latteux [1]. Starting from those, the notions of semitraces, semi-commutative monoids and an order on those monoids are defined. Behaviours of Petri nets are represented by sets of semitraces. Using that tool, properties of Petri nets, mainly concerning determinism, are discussed. Deterministic Petri nets are characterized in terms of their configurations. The present approach is a generalization of the well-known Mazurkiewicz's [7] trace model.

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