The reachability problem for 1-dimensional Pushdown Vector Addition Systems (1-PVASS) is a big open problem. Here I propose another problem, which seems much simpler, but hopefully can shed a light into reachability of 1-PVASS. Instead of 1-PVASS we consider 1-dimensional Grammar Vector Addition Systems, (1-GVASS) which are equivalent wrt. the reachability problem to 1-PVASS.

The problem is formulated as follows: we are given a context-free grammar G with terminals being integers and two natural numbers a, b. The question is whether there exists a witness word \(w \in Z^*\) such that:

- for each prefix v of w the expression (a + the sum of letters of v) is nonnegative;
- a + sum of letters of w = b.