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

Ranko Lazić (1) , Sylvain Schmitz (2, 3)

1 University of Warwick [Coventry]
2 DAHU - Verification in databases
3 LSV - Laboratoire Spécification et Vérification [Cachan]

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.

Mots clés: Linear logic; vector addition systems; fast-growing complexity

Domaines: Logique en informatique [cs.LO]

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⟩