@Unpublished{     leroux:hal-00989109,
  Author        = "Leroux, J{\'e}r{\^o}me and Praveen, M. and Sutre, Gr{\'e}goire",
  Abstract      = "{This paper studies the boundedness and termination problems for vector addition systems equipped with one stack. We introduce an algorithm, inspired by the Karp \& Miller algorithm, that solves both problems for the larger class of well-structured pushdown systems. We show that the worst-case running time of this algorithm is hyper-Ackermannian for pushdown vector addition systems. For the upper bound, we introduce the notion of bad nested words over a well-quasi-ordered set, and we provide a general scheme of induction for bounding their lengths. We derive from this scheme a hyper-Ackermannian upper bound for the length of bad nested words over vectors of natural numbers. For the lower bound, we exhibit a family of pushdown vector addition systems with finite but large reachability sets (hyper-Ackermannian).}",
  affiliation   = "Laboratoire Bordelais de Recherche en Informatique - LaBRI",
  date-added    = "2014-06-26 13:28:27 +0000",
  date-modified = "2014-06-26 13:28:27 +0000",
  hal_id        = "hal-00989109",
  Language      = "Anglais",
  Month         = "May",
  PDF           = "http://hal.archives-ouvertes.fr/hal-00989109/PDF/StackWSTSBoundedness.pdf",
  Title         = "{Hyper-Ackermannian Bounds for Pushdown Vector Addition Systems}",
  URL           = "http://hal.archives-ouvertes.fr/hal-00989109",
  Year          = "2014",
  bdsk-url-1    = "http://hal.archives-ouvertes.fr/hal-00989109",
  File          = "Hyper-Ackermannian Bounds for Pushdown Vector Addition Systems - Leroux, Praveen, Sutre (0) (0) - a - a - v.pdf"
}

@Unpublished{ leroux:hal-00989109, Author = "Leroux, J{\'e}r{\^o}me and Praveen, M. and Sutre, Gr{\'e}goire", Abstract = "{This paper studies the boundedness and termination problems for vector addition systems equipped with one stack. We introduce an algorithm, inspired by the Karp \& Miller algorithm, that solves both problems for the larger class of well-structured pushdown systems. We show that the worst-case running time of this algorithm is hyper-Ackermannian for pushdown vector addition systems. For the upper bound, we introduce the notion of bad nested words over a well-quasi-ordered set, and we provide a general scheme of induction for bounding their lengths. We derive from this scheme a hyper-Ackermannian upper bound for the length of bad nested words over vectors of natural numbers. For the lower bound, we exhibit a family of pushdown vector addition systems with finite but large reachability sets (hyper-Ackermannian).}", affiliation = "Laboratoire Bordelais de Recherche en Informatique - LaBRI", date-added = "2014-06-26 13:28:27 +0000", date-modified = "2014-06-26 13:28:27 +0000", hal_id = "hal-00989109", Language = "Anglais", Month = "May", PDF = "http://hal.archives-ouvertes.fr/hal-00989109/PDF/StackWSTSBoundedness.pdf", Title = "{Hyper-Ackermannian Bounds for Pushdown Vector Addition Systems}", URL = "http://hal.archives-ouvertes.fr/hal-00989109", Year = "2014", bdsk-url-1 = "http://hal.archives-ouvertes.fr/hal-00989109", File = "Hyper-Ackermannian Bounds for Pushdown Vector Addition Systems - Leroux, Praveen, Sutre (0) (0) - a - a - v.pdf" }