# Reachability in Two-Dimensional Unary Vector Addition Systems with States is NL-Complete*

@article{Englert2016ReachabilityIT, title={Reachability in Two-Dimensional Unary Vector Addition Systems with States is NL-Complete*}, author={Matthias Englert and R. Lazic and P. Totzke}, journal={2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)}, year={2016}, pages={1-8} }

Blondin et al. showed at LICS 2015 that two-dimensional vector addition systems with states have reachability witnesses of length exponential in the number of states and polynomial in the norm of vectors. The resulting guess-and-verify algorithm is optimal (PSPACE), but only if the input vectors are given in binary. We answer positively the main question left open by their work, namely establish that reachability witnesses of pseudo-polynomial length always exist. Hence, when the input vectors… Expand

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#### References

SHOWING 1-3 OF 3 REFERENCES

Reachability in Two-Dimensional Vector Addition Systems with States Is PSPACE-Complete

- Mathematics, Computer Science
- 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science
- 2015

Demystifying Reachability in Vector Addition Systems

- Mathematics, Computer Science
- 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science
- 2015