Multiset and K-Subset Transforming Systems
We introduce K-subset transforming systems as a generalization of multiset transformation. A K-subset, which is a generalization of a multiset where “multiplicities” take values in a semiring, is considered by S. Eilenberg. We construct an example of K-subset transforming system which models a chaotic discrete dynamical system. We show that for every basic reaction of multiset transformation we can construct a K-subset transforming system which expresses the multiset transformation. We also show that for every phrase structure grammar there is a K-subset transforming system such that the system simulates derivations of the grammar.
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