Reachability in Two-Dimensional Vector Addition Systems with States: One Test is for Free

by   Jerome Leroux, et al.

Vector addition system with states is an ubiquitous model of computation with extensive applications in computer science. The reachability problem for vector addition systems is central since many other problems reduce to that question. The problem is decidable and it was recently proved that the dimension of the vector addition system is an important parameter of the complexity. In fixed dimensions larger than two, the complexity is not known (with huge complexity gaps). In dimension two, the reachability problem was shown to be PSPACE-complete by Blondin et al. in 2015. We consider an extension of this model, called 2-TVASS, where the first counter can be tested for zero. This model naturally extends the classical model of one counter automata (OCA). We show that reachability is still solvable in polynomial space for 2-TVASS. As in the work Blondin et al., our approach relies on the existence of small reachability certificates obtained by concatenating polynomially many cycles.



There are no comments yet.


page 1

page 2

page 3

page 4


Reachability is Tower Complete

A complete characterization of the complexity of the reachability proble...

Coverability in 1-VASS with Disequality Tests

We show that the control-state reachability problem for one-dimensional ...

The Complexity of Reachability in Affine Vector Addition Systems with States

We give a trichotomy on the complexity of integer reachability in vector...

The Polynomial Complexity of Vector Addition Systems with States

Vector addition systems are an important model in theoretical computer s...

Affine Extensions of Integer Vector Addition Systems with States

We study the reachability problem for affine Z-VASS, which are integer v...

Reachability in Vector Addition Systems is Primitive-Recursive in Fixed Dimension

The reachability problem in vector addition systems is a central questio...

Universality Problem for Unambiguous VASS

We study languages of unambiguous VASS, that is, Vector Addition Systems...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.