Closure Properties of Deterministic Petri Nets

Deterministic Petri nets, as introduced in Vidal-Naquet's thesis [V] are studied here. We investigate systematically their closure properties under the standard language theoretical operations and prove in particular that the complement of a lan-guage of a deterministic net is always the language of a Petri net — which improves on both sides Hack's result on the complementation closure of free Petri net languages [H] —.

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