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arXiv · 2401.16095

On the Separability Problem of VASS Reachability Languages

Eren Keskin·Roland Meyer
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Abstract

We show that the regular separability problem of VASS reachability languages is decidable and $\mathbf{F}_{\omega}$-complete. At the heart of our decision procedure are doubly-marked graph transition sequences, a new proof object that tracks a suitable product of the VASS we wish to separate. We give a decomposition algorithm for DMGTS that not only achieves perfectness as known from MGTS, but also a new property called faithfulness. Faithfulness allows us to construct, from a regular separator for the $\mathbb{Z}$-versions of the VASS, a regular separator for the $\mathbb{N}$-versions. Behind faithfulness is the insight that, for separability, it is sufficient to track the counters of one VASS modulo a large number that is determined by the decomposition.

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Eren Keskin, Roland Meyer. 2024-01-29. On the Separability Problem of VASS Reachability Languages. https://arxiv.org/abs/2401.16095

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