Regular Separability in Büchi VASS

Abstract

We study the (ω-)regular separability problem for Büchi VASS languages: Given two Büchi VASS with languages L1 and L2, check whether there is a regular language that fully contains L1 while remaining disjoint from L2. 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 L2. Based on this, we derive a (sound and complete) notion of inseparability witnesses, non-regular subsets of L1. Finally, we show how to symbolically represent inseparability witnesses and how to check their existence.