On Functions Weakly Computable by Pushdown Petri Nets and Related Systems
We consider numerical functions weakly computable by grammar-controlled vector addition systems (GVASes, a variant of pushdown Petri nets). GVASes can weakly compute all fast growing functions $F_α$ for $α<ω^ω$, hence they are computationally more powerful than standard vector addition systems. On the other hand they cannot weakly compute the inverses $F_α^{-1}$ or indeed any sublinear function. The proof relies on a pumping lemma for runs of GVASes that is of independent interest.
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