It is shown that the boundedness problem for a certain class of basic object nets and a corresponding class of multiset rewriting systems is decidable. To achieve this result Dickson's Lemma for a certain class of multisets, and a modified Karp Miller algorithm, is applied. This presents another class of nets with different decidability behaviour for reachability and boundedness.
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This paper introduces higher-order Petri nets based on multiset rewriting. Some variations of the firing rule for high-level Petri nets following the nets-within-nets paradigm, i.e. allowing Petri nets as tokens, are discussed. All considerations keep in mind the possibile existence of a universal higher-order Petri net.
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