Regular Separability in Büchi VASS

Pascal Baumann, Roland Meyer, Georg Zetzsche

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.