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

07/17/2020
by   Jerome Leroux, et al.
0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

03/13/2020

Reachability is Tower Complete

A complete characterization of the complexity of the reachability proble...
02/18/2019

Coverability in 1-VASS with Disequality Tests

We show that the control-state reachability problem for one-dimensional ...
09/05/2019

The Complexity of Reachability in Affine Vector Addition Systems with States

We give a trichotomy on the complexity of integer reachability in vector...
07/01/2019

The Polynomial Complexity of Vector Addition Systems with States

Vector addition systems are an important model in theoretical computer s...
09/26/2019

Affine Extensions of Integer Vector Addition Systems with States

We study the reachability problem for affine Z-VASS, which are integer v...
03/20/2019

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

The reachability problem in vector addition systems is a central questio...
07/21/2020

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.