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 propositional contractive linear logic is Ackermann-complete.
翻译：我们研究了矢量添加系统分支扩展分支的可达性问题的复杂性,这使我们能够为碎片和假设线性逻辑变体得出新的非元素复杂度。我们表明,多倍化指数碎片的可变性已经在方形案例中是陶塔硬的,因此是非元素的。我们将这一下限与全方位线性线性逻辑相匹配,证明了其塔级完整性。我们还表明,假设线性线性线性逻辑的可选性是Ackermann完全的。
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