The Reachability Problem for Two-Dimensional Vector Addition Systems with States - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of the ACM (JACM) Année : 2021

The Reachability Problem for Two-Dimensional Vector Addition Systems with States

Michael Blondin
Matthias Englert
  • Fonction : Auteur
  • PersonId : 857946
Stefan Göller
  • Fonction : Auteur
  • PersonId : 1231450
Christoph Haase
  • Fonction : Auteur
  • PersonId : 1303275
Pierre Mckenzie
  • Fonction : Auteur
  • PersonId : 1089669

Résumé

We prove that the reachability problem for two-dimensional vector addition systems with states is NL-complete or PSPACE-complete, depending on whether the numbers in the input are encoded in unary or binary. As a key underlying technical result, we show that, if a configuration is reachable, then there exists a witnessing path whose sequence of transitions is contained in a bounded language defined by a regular expression of pseudo-polynomially bounded length. This, in turn, enables us to prove that the lengths of minimal reachability witnesses are pseudo-polynomially bounded.
Fichier principal
Vignette du fichier
final_personal_version.pdf (1.03 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04270941 , version 1 (13-11-2023)

Licence

Paternité

Identifiants

Citer

Michael Blondin, Matthias Englert, Alain Finkel, Stefan Göller, Christoph Haase, et al.. The Reachability Problem for Two-Dimensional Vector Addition Systems with States. Journal of the ACM (JACM), 2021, 68 (5), pp.1-43. ⟨10.1145/3464794⟩. ⟨hal-04270941⟩
37 Consultations
7 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More