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Non-Elementary Complexities for Branching VASS, MELL, and Extensions (1401.6785v3)
Published 27 Jan 2014 in cs.LO
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.