Computer Science > Computational Complexity
[Submitted on 13 May 2019 (v1), last revised 2 Jul 2020 (this version, v3)]
Title:On Affine Reachability Problems
View PDFAbstract: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.
Submission history
From: Stefan Jaax [view email][v1] Mon, 13 May 2019 16:05:10 UTC (80 KB)
[v2] Tue, 21 Jan 2020 11:15:04 UTC (42 KB)
[v3] Thu, 2 Jul 2020 16:10:32 UTC (132 KB)
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