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Complexity of the PVAS reachability problem

Ascertain the exact computational complexity of the reachability problem for priority vector addition systems (PVAS).

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Background

The paper extends key VAS results to PVAS, including flattability for semilinear reachability relations and the existence of semilinear inductive invariants. Despite these advances, the authors note that the precise complexity of PVAS reachability is not known.

In contrast, the reachability problem for standard VAS has a well-established complexity (Ackermann-complete). Determining the complexity for PVAS remains an open task.

References

This leaves two main unknowns for PVAS which are known for VAS: 1) The decidability of the semilinearity problem, that is, given a PVAS, decide if its reachability relation/set is semilinear. 2) The complexity of the reachability problem.

We leave these as future work.

— Flattability of Priority Vector Addition Systems (2402.09185 - Guttenberg, 14 Feb 2024) in Section Conclusion