Universality Problem for Unambiguous VASS

Wojciech Czerwiński (1) , Diego Figueira (2, 3) , Piotr Hofman (1)

1 UW - University of Warsaw
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique
3 CNRS - Centre National de la Recherche Scientifique

We study languages of unambiguous VASS, that is, Vector Addition Systems with States, whose transitions read letters from a finite alphabet, and whose acceptance condition is defined by a set of final states (i.e., the coverability language). We show that the problem of universality for unambiguous VASS is ExpSpace-complete, in sheer contrast to Ackermann-completeness for arbitrary VASS, even in dimension 1. When the dimension d is fixed, the universality problem is PSpace-complete if d ≥ 2, and coNP-hard for 1-dimensional VASS (also known as One Counter Nets).

Mots clés: unambiguity; vector addition systems; universality problem; and phrases unambiguity; universality problems

Domaines: Théorie et langage formel [cs.FL]

Wojciech Czerwiński, Diego Figueira, Piotr Hofman. Universality Problem for Unambiguous VASS. 2020. ⟨hal-02483495v2⟩