Hyper-Ackermannian Bounds for Pushdown Vector Addition Systems

Jérôme Leroux (1) , M. Praveen (1) , Grégoire Sutre (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

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).

Domaines: Logique en informatique [cs.LO]; Complexité [cs.CC]

Jérôme Leroux, M. Praveen, Grégoire Sutre. Hyper-Ackermannian Bounds for Pushdown Vector Addition Systems. CSL-LICS 2014 - 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.Article 63, ⟨10.1145/2603088.2603146⟩. ⟨hal-00989109⟩