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Non-Elementary Complexities for Branching VASS, MELL, and Extensions

Ranko Lazić 1 Sylvain Schmitz 2, 3, * 
* Corresponding author
2 DAHU - Verification in databases
LSV - Laboratoire Spécification et Vérification [Cachan], Inria Saclay - Ile de France
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.
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Submitted on : Wednesday, October 22, 2014 - 6:46:59 PM
Last modification on : Saturday, June 25, 2022 - 7:41:02 PM

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Ranko Lazić, Sylvain Schmitz. Non-Elementary Complexities for Branching VASS, MELL, and Extensions. Joint meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science, Jul 2014, Vienna, Austria. pp.61:1--61:1, ⟨10.1145/2603088.2603129⟩. ⟨hal-01076694⟩



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