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.

Fixed Fig. 3 thanks to Hiromi Tanaka

References in corpus (2)

• Ackermannian and Primitive-Recursive Bounds with Dickson's Lemma
• Complexity Hierarchies Beyond Elementary

Cited by in corpus (5)

• Complexity Hierarchies Beyond Elementary
• A note on undecidability of propositional non-associative linear logics
• Computational Complexity of Deciding Provability in Linear Logic and its Fragments
• An Approach to Regular Separability in Vector Addition Systems
• Branch-Well-Structured Transition Systems and Extensions