Continuous Pushdown VASS in One Dimension are Easy

A pushdown vector addition system with states (PVASS) extends the model of vector addition systems with a pushdown stack. The algorithmic analysis of PVASS has applications such as static anal- ysis of recursive programs manipulating integer variables. Unfor- tunately, reachability analysis, even for one-dimensional PVASS is not known to be decidable. We relax the model of one-dimensional PVASS to make the counter updates continuous and show that in this case reachability, coverability, and boundedness are decidable in polynomial time. In addition, for the extension of the model with lower-bound guards on the states, we show that coverability and reachability are in NP, and boundedness is in coNP.