[Nick87633]

I did a bit of noodling on the wikipedia page for VASS... Maybe I can make an example with software context... and this is probably wrong in some way so take with a grain of salt!

Take as an example a directed graph representing a state transition diagram of a state machine. The machine has some integers (we can call it memory) as its internal state as well as having its graph location. Each state transition moving from one node of the graph on its available outbound transitions has an associated effect on the integers in memory (addition or subtraction particular to each state transition).

The VASS reachability problem: Given a state (memory values and location in the state graph), can you reach some other arbitrarily chosen state by navigating the transition graph, while also not allowing the integers in memory to become negative. What is the guaranteed maximum time complexity for deciding whether any arbitrarily chosen final state is reachable?

VAS - the same problem but without the directed graph restricting access to vectors. I think this one can be intuited as a "vector walk" that must stay in the positive quadrant going from a given start location to a given end location and a list of available vectors that can be used to move around in the space.

Edit: if someone more knowledgeable is reading, please let me know anything incorrect and I will delete or edit.