Decidability of semilinearity for Priority VAS

Decide whether, for a given priority vector addition system (PVAS), its reachability relation or reachability set is semilinear; that is, determine the decidability of the semilinearity problem for PVAS.

Background

The paper proves that semilinear reachability relations in Priority VAS (PVAS) are flattable and that PVAS admit semilinear inductive invariants. While analogous results are known for classical VAS, the authors highlight that certain foundational questions for PVAS remain unresolved.

Specifically, the semilinearity problem—deciding whether the reachability relation/set of a given PVAS is semilinear—has been resolved for VAS but not for PVAS. The authors identify this as one of two main unknowns left open by their work.