Regular Separability in B\"{u}chi VASS

Abstract

We study the ($\omega$-)regular separability problem for B\"uchi VASS languages: Given two B\"uchi VASS with languages $L_1$ and $L_2$, check whether there is a regular language that fully contains $L_1$ while remaining disjoint from $L_2$. We show that the problem is decidable in general and PSPACE-complete in the 1-dimensional case, assuming succinct counter updates. The results rely on several arguments. We characterize the set of all regular languages disjoint from $L_2$. Based on this, we derive a (sound and complete) notion of inseparability witnesses, non-regular subsets of $L_1$. Finally, we show how to symbolically represent inseparability witnesses and how to check their existence.