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

Ranko Lazić 1 Sylvain Schmitz 2, 3
3 DAHU - Verification in databases
CNRS - Centre National de la Recherche Scientifique : UMR8643, Inria Saclay - Ile de France, ENS Cachan - École normale supérieure - Cachan, LSV - Laboratoire Spécification et Vérification [Cachan]
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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https://hal.archives-ouvertes.fr/hal-01168290
Contributor : Sylvain Schmitz <>
Submitted on : Thursday, June 25, 2015 - 3:35:24 PM
Last modification on : Thursday, February 7, 2019 - 5:29:33 PM

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Ranko Lazić, Sylvain Schmitz. Non-Elementary Complexities for Branching VASS, MELL, and Extensions. ACM Transactions on Computational Logic, Association for Computing Machinery, 2015, 16 (3:20), pp.1--30. ⟨10.1145/2733375⟩. ⟨hal-01168290⟩

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