# The Complexity of Reachability in Affine Vector Addition Systems with States

@article{Blondin2020TheCO, title={The Complexity of Reachability in Affine Vector Addition Systems with States}, author={Michael Blondin and Mikhail Raskin}, journal={Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science}, year={2020} }

Vector addition systems with states (VASS) are widely used for the formal verification of concurrent systems. Given their tremendous computational complexity, practical approaches have relied on techniques such as reachability relaxations, e.g., allowing for negative intermediate counter values. It is natural to question their feasibility for VASS enriched with primitives that typically translate into undecidability. Spurred by this concern, we pinpoint the complexity of integer relaxations w.r…

## 4 Citations

On Affine Reachability Problems

- MathematicsMFCS
- 2020

A number of complexity results are obtained, including NP-completeness of the mortality problem for matrices with determinants +1 and 0, and algorithmic problems in finitely generated semigroups of 2-dimensional upper-triangular integer matrices.

The ABCs of petri net reachability relaxations

- Computer ScienceACM SIGLOG News
- 2020

This work surveys relaxations that alleviate the tremendous complexity of deciding configuration reachability in classical Petri nets and for extensions with affine transformations, branching rules and colored tokens.

Parameterized Repair of Concurrent Systems

- Computer ScienceArXiv
- 2021

It is shown that parameterized deadlock detection can be decided in NEXPTIME for disjunctive systems, vastly improving on the best known lower bound, and that it is in general undecidable for broadcast protocols.

The Well Structured Problem for Presburger Counter Machines

- MathematicsFSTTCS
- 2019

It is shown that it is undecidable for most of the (Presburger-defined) counter machines except for Affine VASS of dimension one, but the strong well structured problem is decidable for all Presburger counter machines.

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