Non-elementary 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 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.