Nonelementary Complexities for Branching VASS, MELL, and Extensions

Abstract

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 T ower -hard already in the affine case—and hence non-elementary. We match this lower bound for the full propositional affine linear logic, proving its T ower -completeness. We also show that provability in propositional contractive linear logic is A ckermann -complete.