The reachability set of every 2-dimensional branching VASS has a computable semilinear representation, so reachability is decidable for this class.
Timed pushdown automata and branching vector addition systems
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On the Reachability Problem for Two-Dimensional Branching VASS
The reachability set of every 2-dimensional branching VASS has a computable semilinear representation, so reachability is decidable for this class.