Reachability in symmetric VASS

TL;DR

This paper studies the reachability problem in symmetric vector addition systems with states (VASS), showing it can be solved in PSPACE for symmetric groups, contrasting with Ackermannian complexity in general VASS.

Contribution

It demonstrates that reachability in symmetric VASS is PSPACE-complete, providing complexity bounds for various group symmetries and their combinations.

Findings

Reachability in symmetric VASS is in PSPACE.

Complexity varies with group symmetry, from trivial to symmetric groups.

Combining trivial and symmetric groups affects problem complexity.

Abstract

We investigate the reachability problem in symmetric vector addition systems with states (VASS), where transitions are invariant under a group of permutations of coordinates. One extremal case, the trivial groups, yields general VASS. In another extremal case, the symmetric groups, we show that the reachability problem can be solved in PSPACE, regardless of the dimension of input VASS (to be contrasted with Ackermannian complexity in general VASS). We also consider other groups, in particular alternating and cyclic ones. Furthermore, motivated by the open status of the reachability problem in data VASS, we estimate the gain in complexity when the group arises as a combination of the trivial and symmetric groups.