分支VASS、MELL和扩展的非初等复杂性
Non-Elementary Complexities for Branching VASS, MELL, and Extensions
摘要：
我们研究了向量加法系统的分支扩展上的可达性问题的复杂性，这使我们能够推导出命题线性逻辑的片段和变体的新的非初等复杂性界。我们证明了乘法指数片段的可证明性在仿射情况下已经是塔硬的，因此是非初等的。我们匹配这个下界的充分命题仿射线性逻辑，证明其塔完全性。我们还证明了命题压缩线性逻辑的可证性是阿克曼完备的。
英文摘要：
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.
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