On Affine Reachability Problems

Stefan Jaax; Stefan Kiefer

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arXiv · 1905.05114

On Affine Reachability Problems

Stefan Jaax·Stefan Kiefer

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Abstract

We analyze affine reachability problems in dimensions 1 and 2. We show that the reachability problem for 1-register machines over the integers with affine updates is PSPACE-hard, hence PSPACE-complete, strengthening a result by Finkel et al. that required polynomial updates. Building on recent results on two-dimensional integer matrices, we prove NP-completeness of the mortality problem for 2-dimensional integer matrices with determinants +1 and 0. Motivated by tight connections with 1-dimensional affine reachability problems without control states, we also study the complexity of a number of reachability problems in finitely generated semigroups of 2-dimensional upper-triangular integer matrices.

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Stefan Jaax, Stefan Kiefer. 2019-05-13. On Affine Reachability Problems. https://arxiv.org/abs/1905.05114

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