A Polynomial-Time Algorithm for Reachability in Branching VASS in   Dimension One
  Branching VASS (BVASS) generalise vector addition systems with states by allowing for special branching transitions that can non-deterministically distribute a counter value between two control states. A run of a BVASS consequently becomes a tree, and reachability is to decide whether a given configuration is the root of a reachability tree. This paper shows P-completeness of reachability in BVASS in dimension one, the first decidability result for reachability in a subclass of BVASS known so far. Moreover, we show that coverability and boundedness in BVASS in dimension one are P-complete as well. 
Stefan G\"oller, Christoph Haase, Ranko Lazi\'c and Patrick Totzke
cs.FL cs.LO