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While Affine VASS of dimension one are not, in general, well structured, we give an algorithm that computes the set of predecessors of a configuration; as a consequence this allows to decide the well structured ... We show that it is undecidable for most of the (Presburger-defined) counter machines except for Affine VASS of dimension one. ... In FST TCS 2002: Foundations of Software Technology and Theoretical Computer Science, 22nd Conference Kanpur, India, December 12-14, 2002, Proceedings, pages 145-156, 2002. 12 Alain Finkel, Jérôme ...arXiv:1910.02736v1 fatcat:y2yt7nrjevd6bhmk5rhnl7ge5e