Abstract
We show that any unbounded function weakly computable by a Petri net or a VASS cannot be sublinear. This answers a long-standing folklore conjecture about weakly computing the inverses of some fast-growing functions. The proof relies on a pumping lemma for sets of runs in Petri nets or VASSes.
Work supported by the ReacHard project, ANR grant 11-BS02-001-01.
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Leroux, J., Schnoebelen, P. (2014). On Functions Weakly Computable by Petri Nets and Vector Addition Systems. In: Ouaknine, J., Potapov, I., Worrell, J. (eds) Reachability Problems. RP 2014. Lecture Notes in Computer Science, vol 8762. Springer, Cham. https://doi.org/10.1007/978-3-319-11439-2_15
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