# Nonelementary Complexities for Branching VASS, MELL, and Extensions

@article{Lazic2015NonelementaryCF, title={Nonelementary Complexities for Branching VASS, MELL, and Extensions}, author={Ranko Lazic and Sylvain Schmitz}, journal={ACM Transactions on Computational Logic (TOCL)}, year={2015}, volume={16}, pages={1 - 30} }

We study the complexity of reachability problems on branching extensions of vector addition systems, which allows us to derive new non-elementary complexity bounds for fragments and variants of propositional linear logic. We show that provability in the multiplicative exponential fragment is Tower-hard already in the affine case—and hence non-elementary. We match this lower bound for the full propositional affine linear logic, proving its Tower-completeness. We also show that provability in…

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