NP-hardness of reachability in unary ultraflat 3-VASS

Establish whether the reachability problem in unary ultraflat 3-dimensional Vector Addition Systems with States (ultraflat 3-VASS), where the underlying structure is an ultraflat (simple linear path) scheme with zero-effect inter-cycle transitions, is NP-hard.

Background

The authors prove NP-completeness of reachability for unary ultraflat 4-VASS by constructing gadgets and employing the controlling-counter technique, thereby answering a question posed by Leroux for dimension 4.

They conjecture that the same NP-hardness holds already in dimension 3, which would further sharpen the complexity boundary for ultraflat systems.