The reachability problem for branching vector addition systems requires doubly-exponential space

Branching vector addition systems are an extension of vector addition systems where new reachable vectors may be obtained by summing two reachable vectors and adding an integral vector from a fixed finite set. The reachability problem for them is shown hard for doubly-exponential space. For an alternative extension of vector addition systems, where reachable vectors may be combined by subtraction, most decision problems of interest are shown undecidable.